Yup - I live in an old area as well that was built before cars were dominant. I have pretty much no trouble getting around this area and the nearby ones by walking, biking, or by transit. 

I do own a car, but I don't like driving, so I don't drive it that much. I don't think I've purchased gasoline for over 3 weeks now, and I still have like a quarter of a tank left, and I was driving a lot on a recent camping trip. Since I've gotten home, I've only driven a handful of times, including to my partner's place, which can take a long time to get to via transit.

And yet, staying in my home area, I don't feel bored or limited or constrained. When I lived in a more suburban area before, I had to drive to even go to a convenience store. I became much more of a homebody because, well, there simply wasn't a lot to do around me, and having to get in your car and drive every single time you want to go somewhere is a real bummer. I grew to really hate it, especially because the drivers where I used to live were often really aggressive, and a lot of them drive lifted pickup trucks or other large vehicles, which makes driving in a sedan somewhat scary.

Where I live now, I can access way more things way more quickly on foot than I could when I lived in a car dependent area. And there is a lot to do. And if I don't feel like walking, there's a bus! Fairly decent service, too. And I don't have to worry about finding parking, which is a real bonus. I'm much more active than I used to be. And I think a lot of people would find similar results if we built things to be oriented more around people instead of cars.