The funny thing about this is, you received answers to your 4 questions in the order I would have chosen to live in each city. Philadelphia & St Louis, followed distantly by Milwaukee, and finally Indianapolis.
To answer your question, there are some small homes near the medical campus but it's mostly blue collar and a few medical students. If you want to live in a nice place downtown, you'll probably have to rent. The most popular among young rich professionals is the Gardens of Canal Court, within walking distance of the medical center. It is quiet and people keep to themselves. Rent runs about $1000/mo for a 1 or 2 bedroom 1000 sq ft apt. Some other options are high rise apartments directly downtown such as Riley Towers and Canal Square. They are cheaper, around $700/mo. There are also condos you can purchase along the canal, although they are horribly overpriced (around $450,000 for 1 floor, not sure of the sq footage but I can tell from the outside that it's small). I have no idea who buys those condos but I've never met anyone in the medical field who lived there.
Most medical professionals live away from downtown, since the highways lead conveniently to the medical center. NW is the most expensive area to live in Indy. The community is snobbish and there are a lot of young rich teenagers hanging around that area. Personally I'm irritated by 16 year old boys pimping up their cars and speeding down the road flashing daddy's money. But whatever. There are residents living in the area, though I think it's so they can say they live in the most expensive part of town.
Meridian Street, about halfway between downtown and the north side, is the area of "old money". Plenty of medical professionals living in that area. The houses are old & not very big by today's standards, but living there is all about the status and the community.
Avoid Broad Ripple. High crime due to the number of drunks.
The east side is somewhat run-down. I don't know anyone living there. It is noted for the growing Hispanic community. (I've only seen a few Hispanics there, but people around here are so fearful of non-Caucasians that it has been labeled as the dangerously growing Hispanic population)
The south side is what the people on the north side love to call "white trash". I disagree. The people are poor there, but they don't behave like "trailer trash". I would say the community there is more down-to-earth. There are some medical professionals living on the south side. Housing is cheaper there.
Good luck; you've already gotten far more information than anyone was willing to give me when I first moved here. They're not very welcoming to "outsiders" around here.