. . . 

Cooking time.

Sure, why not. Ignoring fixed ASIs, and I'm going more for mechanical synergy than theme here (though not ignoring theme completely.)

Astral Elf - Evoker Wizard (Astral Fire combos with Potent Cantrip for a damage type wizards usually don't get, and depending on your DM's permissiveness may work with Empowered Evocation as well.)
High Elf - Arcane Trickster (pick up a Bladetrip with your racial and you'll do a ton of sneak attack.)
Wood Elf - Beastmaster Ranger (can't beat the classics. Also, speed boost works with Roving.)
Drow - Fiend Warlock (thematically fitting, plus an extra Darkness/Devil's Sight when you need it.)
Eladrin - Stars or Land Druid (thematic, teleportation shores up a key druid weakness, and you get a strong use for your bonus action when your class doesn't need it.)
Shadar-kai - Bladesinger, Hexblade or Swords Bard (their tanky teleport rewards a gish build.)
Sea Elf - honestly I'm not too interested in this one. Even for an aquatic campaign I rank this one of the least interesting races. Eldritch Knight maybe?

Assuming you're also using Tasha's and can allocate the attribute points however you want, you can kinda do whatever you want.  But here are my thoughts-

• Dark Elf - Cleric, but really only because you get access to Faerie Fire which is new to Clerics.  It's also lore friendly.  Wizard or Sorcerer would also be good.
• High Elf - Wizard.  You get a free extra cantrip but INT is your spell casting attribute for it.  So if it's something that requires an attack roll or saving throw, you'll want to have high INT, so probably wizard or artificer.  There are plenty of cantrips on the wizard list that don't though but they're generally more flavorful.  I guess if you want a druid with minor  illusion or something, this is a great way to go.
• Wood Elf - Druid, but only because it's on theme.  Bladesinger wizards can put to use the extra move speed too.  Their big things are weapon training which casters don't need, extra move speed which casters don't need, and mask of the wild which casters don't really need either.
• Pallid Elf - Cleric I suppose but nothing really here is particularly good for any class.  You'd gain access to to 2 spells not on the cleric list but otherwise nothing here is great.  Sleep is only good at very low levels. Invisibility is good but it's self only and only once per long rest.  You can't technically add these to your spell list either.
• Mark of Shadow - Bard, really just for Cunning Intuition.  Adding a d4 to performance is a nice bonus for a bard.  The extra spells are largely already on the bard list but at least you get them for free.  Otherwise, druids miss out on a lot of these spells so that could be good.
• Astral - Druid.  You get a free cantrip (although none of the 3 are super good) and you get a free teleport on a bonus action.  Most casters get misty step but druids do not.  Giving yourself a similar ability that you can use a few times per long rest is great.  Astral trance gives you a free skill, and weapon or tool proficiency.  This is pretty good for anyone.
• Eladrin - Moon druid and Bladesinger wizards can both use the fey step versions particularly well.  Any caster would love the Winter one.
• Sea Elf - Sorcerer?  Honestly, nothing in their kit is particularly amazing to any caster unless it's an underwater campaign.  Then everyone would love it.  Druids can already do a lot of this kind of stuff though.
• Shadar-kai - Bladesinger wizards, or bards.  The free bonus action teleports that make you resistant to damage are good for any caster, but particularly bladesingers and valor or swords bards.  2 tools proficiencies are good for everyone but bards tend to fill the roll of skill monkey so it might be better for them.
• Half-elf - Bard, but only for the extra skill proficiencies.  Really, these are great for any caster.  They get a total of 4 attribute bonuses (+2,+1,+1) to play with where other elves only get 3 (+2,+1).  The wood, drow, and high half-elf variants pretty much are the same as their full elf counterparts.  The exceptions are the mark subraces. 
• Mark of Detection half-elf - Sorcerer.  The Magical Detection feature is amazing for anyone.  Sorcerers, with their limited spells known would love to be able to get those spells for free.
• Mark of the Storm half-elf- Cleric.  You get some spells added to the spell list.  If you're going mark of storm, you are also likely going tempest cleric and there are overlaps.  You do get some new ones though.

Best at what