I live a mile or so from Autostaretx in the Ballard neighborhood. Seattle does have a dense downtown core, visit the amazing new library, the Seattle museum of art and head to Mikes Noodles in the International district for food, all these places are an easy walk from each other. The sculpture park at the north end of the core is also nice and right on the water. The Space Needle and Pike Place are primarily just for tourists...
Outside of downtown, Capitol Hill and Ballard are the fun neighborhoods, both have amazing restaurants and shops. Ballard also has the Chittenden Locks with a fish ladder that will be chock full of salmon mid September. The locks and surrounding botanical garden are one of the most visited sights in Seattle, much much more "Seattle" than the market or Space Needle. Stop at "Totem Fish and Chips" across the street at the far northwestern corner of the parking lot, get some food to go and sit on the lawn at the locks and watch the boats go by.
Outside of the dense downtown area Seattle is surprisingly suburban, single family housing on 5000 SF lots is the norm. I see many Sprinters camping in my area, just keep a low profile and you will fit right in. There are so many local vans no one will pay any attention to you! Yesterday I saw 3 vans parked on the south side of the Ballard community center, walking distance to the locks and restaurants etc. Easy bus rides into downtown.
As far as camping goes you need to be a bit outside of town, further than a commute... North of town is Deception Pass State Park and South is Mt Rainer National Park. There are many others, those two really stand out.