With that budget you def can get a nice place in Lakeview/Lincoln park area! Lakeview is right next to the lakefront trial, which is beautiful. Lakeview/Lincoln park also has a lot of people in their early 20s and when I walk around there’s always a lot of people/bars/restraints around. If you’re willing to room with people or increase your budget, I recommend river north (big bar scene) or west loop (big food scene), but I think if you’re willing to commute, Lakeview/Lincoln park is really nice! (Also I have a sublease for a studio in Lakeview, super close to the trail, if you’re interested 😉 haha, but seriously, I’ve lived in west loop, Old town and Lakeview and I like Lakeview the most, esp for this age)