If you live in the suburbs, allow for parking cost downtown in your calculation. Even at the Federal Building where you can find a limited amount of free parking about 5 blocks away, the lowest cost is $40a month. I have no idea what it is downtown.
That said, it is hard to find an affordable place downtown. Given the need for affordability, I would head south to just over I465 either along I65 or 31 both run straight downtown and have alternative routes in case of accidents. There are new and old along 31 and the area is safe and has a wide variety of services very close. Not a walkable area but nice.
Apartments in the St. Joseph area around 10th and Alabama or slightly north are in a great area and very walkable (I live right in the middle of this area). I especially like the Apollo and Garden Arch(
Van Rooy Properties-Better Rental Living-Indianapolis Apartments) or the Ambassador (
Buckingham Companies - Property Management, Development, Metro Construction Corporation - Apartments for rent in Illinois, Indiana, Kentucky and Ohio). The Apollo used to allow dogs but you would need to check current policies. Buckingham is leasing the Ambassador next to the library and it has been totally renovated. 70% leased right now but you will need to call the rental office for more info. They also rent the Plaza next door. If you find out rents, please post for others.
Note that both companies have a lot of properties and I tried to give you the ones within walking distance. If you do go above I65 (12th street) it is a longer hike but doable except in winter days of heavy snow. A couple of these buildings have new fitness studios that you may enjoy.
You will need to check out any dog and parking issues.
I love being downtown even though I rarely go "downtown". It is so nice not to have to get in a car to get something. The library is a great resource and there are activities each week downtown.
It really depends on what you like to do, where your friends are located, etc. If everyone you know lives on the north side and you dont really want to walk around and enjoy urban living, maybe the suburbs are better. I was the only one in my office living downtown.
If you ever need to get to the airport, a shared limo with pick up and drop off at the door is $12 one way downtown. We also have a local vet on 11th street. Good grocery store, downtown farmers market that should be open all winter too, two big yoga studios (Invoke and City), etc.