You'll be surprised how many Purdue grads you manage to find around here. Though a lot of them do keep that information quiet! It is often assumed that everyone around here is affiliated with IU, but neither my husband nor I went there or are employed there.
There are LOTS of older neighborhoods around here. Near west side, Prospect Hill, Bryan Park, Elm Heights... other spaces that don't have "names" but are great older homes. If you're planning to buy, check out www.homefinder.org
to find Bloomington listings. If your children will be going to public schools at some point, you'll want to pay some attention to what school you're districted to - Rogers/Binford, Childs, and University are widely considered to be the "best".
In general, I would avoid housing right near the area known as "The Hill", which is the public housing area (roughly between 12th and 15th Streets, from Monroe to Illinois). The reputation is worse than the reality, but there are still notably more drugs than you're going to want your kids around. I would also personally avoid anything in about a mile radius from the stadium - LOTS of loud, partying students, and I just don't want to be around that.
Bryan Park area is ideal for many families. It's mostly older houses (typically 1940-1965-ish, with some newer ones thrown in), the lots are genrally big enough to garden on and play in, and Bryan Park is a huge, very kid-friendly park with a public swimming pool, free concerts in the summer, and multiple playground areas.
Elm Heights is a beautiful area, large houses, large yards, very old and well-established, tons of trees... all really great stuff. It's also expensive and the houses there were well out of my price range. If you can afford it, it would be a great place to raise your kids and critters.
If you want a LOT of personal space, you might want to look at houses in Monroe County but outside of Bloomington city limits. I know there are some great houses east of Hwy 446, surrounded by woods, and have a good-sized amount of land. I like to be closer in to everything, but I know others who like living in Ellettsville, which is essentially the suburb of Bloomington, much more rural, and only 15 minutes west of B-town by car. Part of this depends on what you mean by wanting "more land" - our last house was on 1/4 acre, which was more than enough for me, and our current house is on 3/4 acre and only 5 minutes from downtown. I consider this to be a ridiculously HUGE yard, so if you aren't thinking in terms of multiple acres, there's plenty of houses with plenty of space in town.