Highelf level 3 stats: St 12, Dx 18, Co 15, In 18, Wi 14, and Ch 13.
Feats and ASI: I have a selection of feats: ASI In to 20, ASI Dex to 20, Fey touched, Shadow touched, Elven Accuracy, Resilience Con to 16, Mobile and Luck. Invisibility and Misty Step are spells my character will use anyway. The choices here are very difficult with the exception of the Resilience Con.
Multiclassing looks a bit meh to me because due to the restrictions of the Bladesong some stuff from fighters or paladins will fall off. Both classes can provide a +1 AC, a small heal, and one better power of Smite or Action Surge. But it will cause the loss of an ASI too. The paladin would even have to require to move the 14 from Wis to Str and vice versa.
For me, improving the character would be dependant on what the character was all about and not so much on min/maxing it, here's a link to a high elf bladesinger idea I had a while back.
I'm playing a level 7 eladrin bladesinger. I chose Eladrin Sword Wizardry as a feat, but that wouldn't apply to you since you're high elf. It all depends on what you want to improve: damage, AC, etc? Get yourself a good weapon and the green-flame blade cantrip though. It's awesome for a bladesinger and it improves with leveling up.
Well, you don't meet the eladrin prerequisite anyway being high elf. Check with your DM and maybe you can make something similar like a homebrew for High Elf Sword Wizardry. I had to make a homebrew for mine.
It depends a bit on your play style, but if you plan on playing a heavy melee build, here is how I would rank those you mentioned in terms of combat power. I also added a couple to consider in red:
Lucky
Dex ASI
Fey Touched with Silvery Barbs (if you already have SB you can take Dissonant Whispers)
Shadow Touched with False Life (or Cause Fear if you already have False Life)
Int ASI
Warcaster
Metamagic Adept with quicken spell (this lets you get blur or protection from Evil and Good up quicker if your concentration fails)
Gift of the Gem Dragon (if you plan on using Shadow Blade a lot, this is a good feat to pair with it. I don't recommend a shadow-blade focused build on a bladesinger though)
I would not recommend the other feats you mention for the following reasons:
Resilient Constitution is not that great on a bladesinger IMO. It is better on other classes but on a Bladesinger you really can't afford it. When it comes to concentration saves you already have your intelligence boost and things that reduce damage (like a dex ASI) are going to do better. It is also not as good as Warcaster in terms of concentration saves when you do get hit. The extra hit points are less than you can get by casting false life.
Elven Accuracy is not great on a bladesinger either. Your attacks do not hit hard enough that it is ultra-important to land them and you have an even dexterity so you won't benefit from the half ASI. There are few good dexterity half feats, meaning you will go to 19 but then have to waste a point on constitutuion or charisma at the following ASI.
Mobile is bad for a Bladesinger IMO. As a bladesinger you generally want to draw AOOs so they can't be used against your allies that are easier to hit and that hit harder than you. You can do a lot of things with a bladesinger and there are a lot of different builds and the chassis makes for a great tank, controller or blaster but it does not do well as a striker and that is what mobile works really well with.
That is if you are focused on combat. If you are looking at overall gameplay in all three pillars I would move Fey Touched and Shadow Touched to the very top, and also consider Hex with Fey Touched. Another good Bladesinger feat if you are looking at all 3 pillars is Telepathic.
Elven Accuracy is always good for an elf. With bladesinger you have many ways to gain advantage, so it's a good feat for you. There are other very good feats for a bladesinger. Resilience Con or Lucky (good for any character) are great options too.
However, since you have int 18, I would go for the ASI to have int 20 ASAP. It improves your concentration checks, it improves your AC, and since you're a wizard, it improves your spellcasting. And, in my opinion, with the next ASI I would go for Resilence Con.
How can I improve my bladesinger?
Highelf level 3 stats: St 12, Dx 18, Co 15, In 18, Wi 14, and Ch 13.
Feats and ASI: I have a selection of feats: ASI In to 20, ASI Dex to 20, Fey touched, Shadow touched, Elven Accuracy, Resilience Con to 16, Mobile and Luck. Invisibility and Misty Step are spells my character will use anyway. The choices here are very difficult with the exception of the Resilience Con.
Multiclassing looks a bit meh to me because due to the restrictions of the Bladesong some stuff from fighters or paladins will fall off. Both classes can provide a +1 AC, a small heal, and one better power of Smite or Action Surge. But it will cause the loss of an ASI too. The paladin would even have to require to move the 14 from Wis to Str and vice versa.
For me, improving the character would be dependant on what the character was all about and not so much on min/maxing it, here's a link to a high elf bladesinger idea I had a while back.
https://www.dndbeyond.com/forums/d-d-beyond-general/story-lore/110295-robs-unused-character-idea-6-silence-the-mage
Those are some mighty nice starting stats.
I'm playing a level 7 eladrin bladesinger. I chose Eladrin Sword Wizardry as a feat, but that wouldn't apply to you since you're high elf. It all depends on what you want to improve: damage, AC, etc? Get yourself a good weapon and the green-flame blade cantrip though. It's awesome for a bladesinger and it improves with leveling up.
In which book is that eladrin sword wizardry? I find Booming Blade great too because it gives a little bit battlefield control too.
I searched for wizard feats, it came up, and I ran it by my DM who approved. I found it on dnd4.fandom.com.
Booming Blade is good. I've found Spirit Shroud and Mirror Image to be useful as well.
That was a D&D 4e feat. For 5e I can not find anything like this.
Well, you don't meet the eladrin prerequisite anyway being high elf. Check with your DM and maybe you can make something similar like a homebrew for High Elf Sword Wizardry. I had to make a homebrew for mine.
Wow, with those stats why would you need to multiclass?
Due to its restrictions, multiclass seems not to be that good on a bladesinger.
The selection of incredible feats makes it challenging to pick which one. The only sure pick is the Resilience Con.
It depends a bit on your play style, but if you plan on playing a heavy melee build, here is how I would rank those you mentioned in terms of combat power. I also added a couple to consider in red:
Lucky
Dex ASI
Fey Touched with Silvery Barbs (if you already have SB you can take Dissonant Whispers)
Shadow Touched with False Life (or Cause Fear if you already have False Life)
Int ASI
Warcaster
Metamagic Adept with quicken spell (this lets you get blur or protection from Evil and Good up quicker if your concentration fails)
Gift of the Gem Dragon (if you plan on using Shadow Blade a lot, this is a good feat to pair with it. I don't recommend a shadow-blade focused build on a bladesinger though)
I would not recommend the other feats you mention for the following reasons:
Resilient Constitution is not that great on a bladesinger IMO. It is better on other classes but on a Bladesinger you really can't afford it. When it comes to concentration saves you already have your intelligence boost and things that reduce damage (like a dex ASI) are going to do better. It is also not as good as Warcaster in terms of concentration saves when you do get hit. The extra hit points are less than you can get by casting false life.
Elven Accuracy is not great on a bladesinger either. Your attacks do not hit hard enough that it is ultra-important to land them and you have an even dexterity so you won't benefit from the half ASI. There are few good dexterity half feats, meaning you will go to 19 but then have to waste a point on constitutuion or charisma at the following ASI.
Mobile is bad for a Bladesinger IMO. As a bladesinger you generally want to draw AOOs so they can't be used against your allies that are easier to hit and that hit harder than you. You can do a lot of things with a bladesinger and there are a lot of different builds and the chassis makes for a great tank, controller or blaster but it does not do well as a striker and that is what mobile works really well with.
That is if you are focused on combat. If you are looking at overall gameplay in all three pillars I would move Fey Touched and Shadow Touched to the very top, and also consider Hex with Fey Touched. Another good Bladesinger feat if you are looking at all 3 pillars is Telepathic.
Elven Accuracy is always good for an elf. With bladesinger you have many ways to gain advantage, so it's a good feat for you. There are other very good feats for a bladesinger. Resilience Con or Lucky (good for any character) are great options too.
However, since you have int 18, I would go for the ASI to have int 20 ASAP. It improves your concentration checks, it improves your AC, and since you're a wizard, it improves your spellcasting. And, in my opinion, with the next ASI I would go for Resilence Con.
Lvl 4 EA +1 to Int. pairs well with Shadow Blade at these levels and extra attack at lvl 6
Lvl 8 FT +1 Int. caps Int. gives you 21AC with Studded Leather and Bladesong, you want to be focusing on spells at this point
Lvl 12 Res. Con. gives you a +12 on Concentration Saves with Bladesong and more HP
18 Dex is plenty for a Bladesinger and don't multiclass