Walk. Just like I would hike when I lived rurally, walk. There are trails along the River and through the woods, even in the middle of town. But there’s also sidewalks. A town common. Parks. Several playgrounds have pickup basketball if your knees are better than mine, or there’s a track within an easy walk for some more regimented exercise. Our favorite activity starting during Covid is to walk around our city, seeing the sights. It was a great chance to talk with my kids for hours, before they went off to college. And yes we played Pokémon go as something to do while walking (and a game like that is much better in cities), and met several groups of people that way. If that game is too nerdy or childish, there are apps that gamify walking in various ways. If you’re willing to spend a little, sometimes we would stop at a convenience store for a soda or something, but not always.
When I lived in the major city, it was the same only much more. Every weekend had a festival (free). Every weekend had a band playing somewhere outside free. Every weekend had some big free event at multiple parks. Every Wednesday was free museums. Walking the waterfront is really cool and entirely free. Tourist areas sometimes have street entertainers, free. My city is very walkable and has many colleges: every weekend had some event at some college. My city has a lot of history and tourism, organized as a free “trail” and with most historic things free. There are things like a sailing ship that is free to see: you would have to pay for the museum and gift shop but why would you? Read the historic plaques. If a building or something looks historic, look it up.
For a relatively small amount of money, one of my favorite activities was the farmers market: it was huge and cheap (although I haven’t been in many years). Sometimes I just wanted to walk around and see everything (that shopping is selling whole goats?), or I could buy a week’s worth of veggies fresh from the farm for pennies on the dollar. And connect that back to food prep: when I didn’t have much money or time, I’d take all Saturday, goto the farmers market, come back and put together a giant salad for the week, a pasta salad for the week, maybe marinate some meat in some ingredients I bought- basically get half my cooking and shopping out of the way, dirt cheap
For a relatively small amount of money, much cheaper than operating a car, I usually had a subway pass. The core of that major city is very walkable, but the pass opened the entire city by just hopping on a convenient train without having to think about spending in the moment.
As far as staying in the small apartment goes, being in an urban area means gigabit fiber, which I guess a lot of people still don’t have. Being a first class citizen online is priceless and opens a lot of free (after your internet bill) activities involving sitting at your desk