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I have lived on Capital Hill and in the Seattle environs for fourteen years. The hill is gay friendly, and all of Seattle is gay friendly. In my experiences the price for square foot for my room on Capital Hill was pretty high. There is a city park, pretty small, Volunteer park. It has an art museum and water fountains, etc.
I lived by Northgate in Seattle close to 145th street, it was within walking distance to Hamlin Park in the next city (Shoreline) and got a whole house (three bedrooms, large yard for a dog, 22nd Ave NE) for $1,350. I took over the lease after staying there two years with roomates. I stayed five years due to my love of the woods, actual moss covered logs woods. Fifteen minutes to downtown with express lanes in the morning. There is a pea patch, Jackson Park P-Patch Community Garden. I would wait and find a house and I would not want to stay at the Jackson Park apartments adjacent to the park. OK, I'll tell you a secret, behind that there is an unnamed park with trails and an actual creek, I have seen an owl there just looking at me by the creek; I am describing the woods between the pea patch and golf course. This is about ten blocks from Hamlin Park.
There is also Discovery park, a retired military base, with miles and miles of trails and a lighthouse. I mention this after the area near 145th Street because travel time from Discovery Park to downtown (International Film Festival, gay bars on the hill) is longer during rush hour. If you bike, you might like Discovery Park better. That is in the Magnolia area, I include links some of what I've described.
Bothell is pretty far from town, as is Bellevue across the toll bridge. I would call those and Federal Way as strip malls from hell. Everett if pretty far, about an hour, to get to a Capital Hill bar.
I moved here for the proximity to the Olympic Peninsula. No matter what suburb you get to, the hikes around here are astounding. I have a list of my favorites here: www.lake22.com