Hi, I'm in city accommodation (Carpenter House) and, although I'd initially wanted campus accommodation, I'm honestly so glad I'm in the city (it was 7th on my list). If you don't mind a bit of a commute (10/15 mins by bus (buses are frequent) or a 35 ish minute walk (there's a really pretty route that goes through some National Trust fields – full of buttercups at the moment!)) and don't mind not being on campus, then I'd really recommend it.
Close to the supermarket! Big Sainsbury's is like 7 minutes away, and Lidl is 10 mins along the river by bike. Much cheaper than the "Fresh" mini supermarket (coop type thing) on campus, and much easier than dragging all your food shopping back up to campus.
In the city! Bath is such a lovely city, really pretty, lots of shops, cafés etc. and it's really nice to be able to explore and get to know the area a bit. And close to the train station etc. so going home or having people come to visit is much less hassle than trying to take your bags and suitcases to and from campus.
I don't know much about the other accommodations (on or off campus) so can't really give much insight here, but Carpenter House is a pretty standard, reasonably cheap option, seems a bit nicer than Norwood House and probably Eastwood too (both on-campus options for the same rent budget).
Hope this helps a bit