As someone who's traveled quite a bit, I love doing this but I should also warn everyone to make sure they're in a place where it's safe to do so. While most tourist destinations are mostly fine, you don't want to end up in a random shady neighborhood in certain cities - even touristy ones (Barcelona, Paris, etc). It doesn't matter that 20 years ago you did it and it was fine, things have changed.

I did that once about twenty years ago. I was in Seoul for a few days for work, and I had the last day free before my plane out in the evening. Without checking a map or guidebook, I got on the subway, rode a few stops, went up to street level, and wandered around; I repeated this four or five times. Other than one nondescript office district, every area I emerged in was interesting: a wholesale textile market, an upscale residential neighborhood, a lively commercial district. Though I don’t know the names of the places I visited, I still remember them all these years later.

What are some of your experiences with this?

I can say I've had good and bad - I've wondered through cities with no direction and found -- nothing, two that come to mind are Paris and Barcelona. I'm sure there is interesting stuff to be found here and there but mostly, outside of the main attractions, I found the rest not much more interesting than American suburbia. Yes, I'm glad I saw it to basically see that "life is life". There's the interesting coast, or the restaurant row that's already on the tourist map, then there's the living areas where every block or two there's a convenience store, another non-descript cafe, a hair salon, etc... Maybe once in a while something sticks out but mostly not.

To be clear, I found both cities amazing. But, the "this city is amazing" parts are the parts listed as must visit. The "get lost parts" less so, with a few exceptions.

I've had more luck doing things further down the list. On 3rd or 4th visit, I'm not doing the top 10 most popular things. I'm down on 40th or 50th or 100th.

This is one of the only sensible comments in this entire thread. Just go wander, talk to and observe people, etc... I've traveled extensively and all of my best experiences are from this sort of thing.