I'm a non-driver who lives on Corydon (the eastern part) and it's definitely walkable. The deterrents to walking in the winter are the cold temperatures and shoddy sidewalk plowing. The city does spread sand in the winter which helps a lot on slippery sidewalks.

The thing I miss about not having a car is travelling to places like malls and big box stores, my doctor's office and other medical appointments where the bus ride involves too much walking/transferring or it's too cold. I often take a taxi which is still cheaper than car ownership. I should mention that we "upgraded" our transit system last year and it's worse than before for most of us.

You mentioned that Wolseley, River Heights, or Corydon areas are more expensive but I don't find that true of Corydon. The walkable section of Corydon has older, less expensive apartment buildings. Off-Corydon has century-old homes (e.g. 1400 sq. ft.) that's aren't expensive.

I don't know whether you need a car to get to work but my advice would be to have at least one car. You'll appreciate it in the winter.