A Brompton is really small when folded. Smaller than a carry-on suitcase by volume. It rolls on little scooter wheels on the rear rack when folded. I bring mine into all the places you just listed on a regular basis, except for a gym. For a restaurant, it typically will fit under a table. At a bar, if you are at a table the previous thing works. I've also had the bar staff offer to stash it inside the store room. If someone you are meeting up with is DD'ing a trunk works as well. I've never been in a store so small I couldn't roll it in, you can just pull the seat up a bit and roll it in front of you.