You should really reconsider your assumption that Brooklyn/New Jersey will be more laid back than Manhattan, especially the Upper West Side. If you are on one of the cross streets on the west side beween 63rd and 120th, it will be just as quiet/laid back as it would be in Brooklyn. However, you'll have easy access to Central Park (6 miles of pavement running and an interior dirt path that you can easily do 4-5 miles on) and Riverside Park and the Hudson River path (~13 miles from the Battery to Fort Tryon). You've also got reasonably quick access to Van Cortlandt Park via the 1 train and the Riverside State Park track, also via the 1 train. If you have a car or a zipcar membership you can get to Rockefeller State Park in ~35 minutes, which is where a lot of the pros and college teams in the area train. In the winter you can purchase passes to work out at the Armory, which is accessible by several trains in about 20 minutes.
In the areas of Brooklyn that are recommended above, you've got Prospect Park, which is 3.5 miles of mostly pavement running-- and a big portion of the path is sloped for drainage, which can cause some people injury problems. You can run to the track in Red Hook (no subway access) but it certainly isn't close (and it's nothing great as far as facilities go-- you'll be lucky if the single bathroom is unlocked and functioning.) The waterfront path that is accessible from DUMBO is nice but tiny, maybe 2 miles of running? To access the path that runs through Bay Ridge to the Verrazano, you're going to be doing a lot of running on roads that have either tons of truck traffic or are still paved with cobblestones from the 19th century.
I love Brooklyn as a place to live, but for running there really is no comparison to the UWS. Add the fact that it is now just as expensive (if not more so) as the UWS-- I would really discourage you from limiting your search to that area. I would only recommend Brooklyn for running if you're just looking to go out for 3-4 miles a few times a week--anything more than that and it gets pretty damn stale.