Congrats on Seattle U!! I earned my undergrad there and had a great experience. I'm sure you will love the law school.
As far as buying a house, the Seattle market is pretty expensive. If you want to be close to the school, and want to find something affordable, you could try finding something in the Central District just East (down Madison) from campus. Historically, this area of town has been seen as the area to stay away from, and as a result, been faily inexpensive. But in the last few years, it has undergone a slight rejuvination with an influx of young people buying up the houses and investing some money into them. The houses there are more expensive than they were, but far less than the other houses in the nearby Capital Hill or Madison Valley/Park neighborhoods.
West Seattle is another option. Very cool, laid back neighborhoods with lots of great restaurants. The housing there is still considered less than most of Seattle. It's also close to Alki Beach with is beautiful. One draw back though is that West Seattle is about a 20-30 minute drive to SU in traffic. Still a nice place though.
Just south of there is White Center. It too has historically been seen as a place not to live, but like the Central District, it is undergoing a huge rejuvination with lots of young people buying up the affordable housing along with new stores and services moving in such as Westwood Village (similar to University Village, just not as posh). It has great restaurants and is located just off both I-5 and 509/99 so getting to SU and downtown is pretty quick by car. By bus it takes about 20-25 minutes to get to SU.
You could also head north and find something in Ballard. Ballard is a great place that used to be pretty affordable. But it is now pretty pricey, though slightly less than other areas.
YOu might also want to check out the Mt. Baker neighborhood. It's located more east towards Lake Washington, but is really nice and has the reputation to be a bit more affordable. I don't know much more about that area though.
Anyway, happy house hunting. And welcome to Seattle!