As someone who lives right by SVH at the moment and as someone who's lived elsewhere and worked downtown, I offer the following advice.
The area direclty north of SVH, actually north of 15th Street, east of Western Avenue, and west of Minnesota Avenue, is a rough neighborhood and has a majority of the crime. South of SVH, you find the Univeristy of Sioux Falls and Augustana College, so the majority of those homes are rentals and depending on the particular block, dumpy and unkept. There are also some very nice home mixed in. The whole area between approximatley Minnesota Avenue, 33rd Street, Western Avenue, and Russell Avenue is an interesting mix.
Getting downtown from the east side or west side is actually six of one, half dozen the other as both are going to be about the same, although coming from the eastside will give you a few more routes to take. I would recommend looking south. There are a few very nice apartment complexes south of 57th Street. One in particular is Lyncrest Apartments, which is a bit off Minnesota Avenue. Ultimately, it will depend on how much you want to spend. Meltdown has it right in pointing you to the Sioux Falls Argus Leader website for some direction and phone numbers. You might also be able to check the KELO TV website as I think they might also have some links. Also, the south side it really growing. You'll be close a lot of parks, it's easy to get to the Mall, lots of restuarants and bars, fitness facilities, the movie theaters, it's easy to the Gary's Gun Shop (the indoor range), and it's close to the Interstate.
My wife and I are going to be moving soon and we're going to be looking down there.