Game Ideas?

I'm looking to make a festival for my next session, but I don't know what kind of games or attractions I would put in. The city is mostly pretty poor, and there isn't often reason to celebrate, so this festival would be a huge deal, and a lot of saved money would go into it. The city is very gritty and sad, so this would be a nice change-up. Any ideas?

Say more about the worldbuilding you've done around this city. What kind of setting is this? The options are going to be different if we're looking at medieval high fantasy versus something more steampunk or something else. What's the geography around the city? Is it a mining town in the mountains, a commercial hub at the major crossroads, a port with a lot of fishing and ships coming and going? What are the major industries in and around the city? A mercantile city would be celebrating different things from, say, an ironworking city, which would celebrate different things from a city that is more economically defined by agriculture. Tying into that, what time of year is it? Is this happening around a major planting season or harvest season? A solstice or an equinox? Does it concide with a high holiday, feast day, or a government holiday?

All of which is to say: What are the values of the people of the city, and in this moment how are those values being expressed? Depending on what you're looking to express, maybe take some inspiration from festivals and activities during the Great Depression. Walk or dance marathons were popular. An endurance competition like that would probably work as a series of Constitution checks (and maybe saves toward the end, to avoid collapsing, fainting, etc.) So were soap box derbys. I'm not sure what set of rolls would apply for crafting the soap box car, but steering would be some kind of Dexterity roll I imagine. Apparently goldfish swallowing was big too. I'm not sure how to flavor that for a D&D setting, but maybe you can do something with it. Plays have always been popular for keeping crowds amused; depending on your setting a traveling troupe could be performing during the festival. Depending on what sort of industry is important to the town, there might be someting to draw from there. A prize pig or biggest squash competition among farmers that the players could participate in judging, maybe. Or if it's a mining town maybe one of the old tapped-out mine shafts is used as a haunted house attraction and as the players go through it they have to find some hidden objects along the way to get a prize for completing the whole haunted tunnel maze?

Call of the Netherdeep and Wild Beyond the Witchlight both start at carnivals/festivals and have suggestions for games if you can get access to either of those

The city is definitely more fantasy. It's an underground city called Solstara that's oppressed by a corrupt and false religion known as the Pythium Orchaia. 63% of the population live in deep poverty, 35% are middle class, and 2% are the elite class. The city is known for its blacksmiths especially, although has only primitive technology. The only more advanced things are lanterns and signs powered by a substance known as Ardent Powder, made from Ardent Crystals that power the city itself. This is a government holiday celebrating the rule of the Pythium Orchaia, but the people hate the religion and are celebrating mostly just to celebrate. It's like when a fair comes to a town for no particular reason. It's difficult to get out or get into the city, so most people have never left. There is little to no water and it's a very cramped space. There are plenty of additional caves dug into the walls of the city though.

Wild Beyond the Witchlight is an excellent official campaign with a carnival of the same name that could work quite well with what you're describing.

You can probably find any number of excellent game ideas based on dice with a quick google. I would say to punctuate the atmosphere with descriptions. Talk about the clashing colors, vibrant atmosphere, delicious food smells, and whatever else. Toss in a mention on how it contrasts the rest of the city. It's all about presentation.