So I'll be starting a new campaign soon and am trying to start off with a bang!

Since my party has done the 1-5 stretch so many times recently, we'll be STARTING this one off at level 5 (There are 4 players).

We did a session 0 and all decided that the party will already be formed from the start. We worked out a group backstory that accounted for their level 1-5 stretch. 

WHAT I HAVE:

1. I want them to start off at a party honoring them for saving the city. My players have expressed interest in having more complex social encounters (think like a social "dungeon") so I thought a big party with the regional nobility could offer that. 

2. The game is going to be primarily character driven with more focus on backstory and less on "main story"

3. I want their to be layers to this "social dungeon" so it isn't just "Accomplish Goal A". I want there to be complications, subplots, intrigue etc...

WHAT I'M LOOKING FOR:

1. Things happening at this party

2. Interesting NPC's and goals

3. Interesting complications

4. Some way to squeeze in a fight

Here's a quick way to add intrigue to the party...

Someone at the party has been replaced by a Doppelganger. The characters are aware of this in some way... maybe they uncovered a secret message in their adventures up to this point, but they have no hint about who the doppelganger is impersonating. Now they have reason to carefully interview every other person present beyond just societal obligation. Now everything another character says matters, because it might be the clue that reveals their deception. Maybe the Doppelganger might be forced to abandon their disguise if the players get too close, so they'll have to keep an eye out for, say... someone they suspect leading one person to a secluded spot, and only one of them returning.

A single Doppelganger isn't much of a challenge to a level 5 party, but you can fix that by either giving them some allies who will show up, or just powering them up a bit... give a Doppelganger a bit more HP and access to some basic spellcasting and you can make them a compelling battle.

This is really funny and kinda my bad for not saying before, but the intro "quest" we made to explain their 1-5 WAS a doppelganger quest and THAT's what they're currently being celebrated for lol.  

That is pretty funny. I don't know if that takes Doppelganger off the table as a viable plot hook, or if it just kind of sets it up more easily.

Unfortunately I think it takes it off the table. In the group backstory, they discovered the Doppelganger impersonating the city leader, found out that a local noble was the mastermind in charge of the swap, killed the doppelganger, let noble escape (possible future villian). Having another Doppelganger would be like "Really, ANOTHER one?" lol

Though that would be unexpected lol

I think the problem is, if you do use a Doppelganger in this scenario, then you're basically locked into a "Doppelganger campaign", where that's just the thing the party is going to to expect to be dealing with from that point onward.

There could be somebody who's sure that someone is a doppelgänger, but they're not.

There're a few options here:

- maybe there are political dissidents who are already against the city and don't like the party for saving it, so they're there to cause trouble, and might start a brawl/lowkey terrorism at this event, or maybe it's to distract from something bigger they're up to...

- this event is a really good opportunity to introduce Npc's like you said, I love the idea of starting off with the party already having achieved something, that's a good way to generate immersion and party cohesion early on. Kudos. Maybe the party meets some Npc's who want to sponsor their escapades in the future ("Congratulations on your recent efforts in the kingdom! How would you like to continue your work under the banner of House Pendragon?" etc.), or maybe they find some nobles who are looking to make reforms in the city and aren't necessarily with or against the party.

- complications might involve something from their earlier quest. Maybe a villain that they thought they had whupped for good was being controlled by a puppet master, who has far greater plans for the kingdom. Perhaps this villain or a servant of his makes an appearance later at this party, mocking the celebration and sowing fear and discord (after that he could disappear or maybe cause a fight, up to you)

- social encounters can be as simple as a conversation, but the nobility always adds a fun twist. some ideas may be for one of the nobles to start hitting on a player. This could cause a scandal, especially if the player is far below the noble's station. Another could be, building off the recruitment idea above, that maybe a noble wants the help of one of the players, but doesn't extend his invitation to the rest of the party. This could sow some interesting intrigue and create an interesting party dynamic early on

In the end, it's your world so do you what you want. You have a great start already, hope this helps! 

Okay, here's my new pitch for a way to get some extra combat into a situation like this...

During the party, there's an alchemist at the party who's trying to get sponsors to help fund their research. Maybe they even try to recruit the party members... they probably don't have the money to fun him on their own, but he wants to at least try and get them on his side so they can use their influence to help him. Anyway, eventually he reaches a point where he's doing a display of what his alchemy can accomplish, so he drinks an experimental potion and accidentally Hulks out and starts smashing things. So the party then has to focus on knocking him unconscious but will be compelled to avoid killing him outright.

Depending on how you write this character, they could be either an absent-minded but helpful ally, or they could be a dishonest charlatan... like a snake-oil salesman. Either way, how the players handle the situation could affect their standing with the nobles... if they took the alchemist's side and tried to hype him up, suddenly they look incompetent when things go sideways.

Different factions want to get in the party's good graces, maybe promising or implying special favors in exchange for the party's endorsement/support. These offers would be mutually exclusive, with the understanding that the party can't support both the Miner's Guild and the Noble's Coalition because both those factions are at each other's throats over a labor dispute, and likewise the illegal Assassin's Guild is looking to ingratiate itself with the wealthy elite of the city and thinks the party can help with their legitimacy problem, but not if the party wants into the Hall of Heroes-- a strictly lawful organization. 

Basically a complex social encounter should come with choices, rewards, and drawbacks for each offer. 

To expand on CharlesThePlant's suggestion, consider using the alignment chart as a guide for creating 4 groups which are utterly incompatible with one another, for various reasons:

Lawful Good
Chaotic Good
Lawful Evil
Chaotic Evil

leave out the neutrals as they get middle-ground - you want 4 groups who despise one another.

(important to note here - "Lawful" does not mean "Obeys the law", it means "Obeys their own laws". Opeuns up what you can work with here)

So Lawful Good might be the miners guild, who have their rules, and fight for the workers to get good conditions and pay.
Lawful Evil might be the Nobles Guild, who want to get rich and who cares who dies, they're peasants.
Chaotic Good might be an activist group akin to Greenpeace, who will do things they thing are right but have no particular lines that the group won't cross
Chaotic Evil might be the merchant guilds, who want to be rich like the nobles, but are underhanded and roguish in their affairs.

Then set up a conflict for each of them:

Miners vs nobles, as discussed in the post above
Nobles vs Activists - activists are claiming the nobles do nothing with their influence to save the whalebears.
Activists vs merchant guilds, activists are blockading their merchant ships and costing them profits
Merchants vs miners guild, the miners guilds are driving the prices of mined goods up, meaning less profit for merchants

Then have each of them approaching the party looking for support, offering assistance, and so on. Party gets a strong say in what becomes of the world around them, based on their decisions. Consider doing plots for what happens if each faction loses the party's support, so basically one thing doesn't happen based on what they pick, the other three do.

Good luck and enjoy!