Uptown, Dinkytown and over by the U. (University of Minnesota). And downtown can be fun.
Brooklyn Park is so so and right next to Brooklyn Center, which can be bad. You should check out Blaine or Maple Grove. Blaine would be less expensive, I think. But it is the hotbed burb at the moment also.
Downtown, if you want to walk to things. There is light rail downtown also as well as Metro Transit busses. Light Rail heads right down to Bloomington to the airport and Mall of America. More lines are in the works though.
I live in Minnesota north of the Twin Cities but I venture there quite often, especially lately.