You can get a place near the UW that ll fit the bill for reasonably cheap, but I think most of what you re going to find around there is going to be geared at college students, who are by-and-large, young.I lived in Maple Leaf, which is North of the U District; it was nice, but dull - very suburban and family-oriented, and not really what I or my friend/roommate were looking for as mid/late 20 s single students. Ravenna, which is more or less adjacent to the U district, is probably a good halfway point, though there are few luxury apartments there (the prices you re talking about for a 1-bedroom would be in the high-end for Seattle). I moved back down to CA and she s staying up there; now she lives in Eastlake, which is just south over the bridge from the U District, and she pays $900 for a vintage, 1920 s studio with hardwood floors and a view of the skyline. Most of the people in her building are grad or postgrad, mid 20 s to mid 30 s.
Fremont is very close to the UW, has several high-end apartment buildings and townhomes, a running trail right along the water, a nice selection of restaurants, and a great Sunday public market.
University District is right by UW.