I haven't looked up King County park rules, and actually don't really know of any such parks in particular. Drones are prohibited in all Seattle and Bellevue city parks, and all Washington state parks.
Drones are permitted at Luther Burbank Park on Lake Washington on Mercer Island, which is pretty scenic and spacious, though can be crowded.
Drones are permitted at Sixty Acre Park in Redmond, but it's a little boring there.
Rattlesnake Lake in North Bend is beautiful for flying over water, but beaches can be busy. Note, I have seen a low flying heli there, who looked to be near 400' over trees.
Other good practice spots are school sports fields after school hours, friends' yards, empty lots.
As for heliports and airfields, my take is to use common sense and judgment if you're a few miles away. I've placed a few calls to private heliports less than five miles from my home, and had a conversation with one of the owners and chopper pilots. He wasn't too concerned about me flying my drone under 400 feet AGL, and as you start flying your drone more, you'll realize it's usually pointless to go more than 200-300ft very often, because there's really nothing very interesting to see or photograph that high. Most often when I've wanted to climb high above my take off point, it was to track along a hillside, anyway.