Middle Fork or Denny Creek are probably your closest options. If you're already driving from Yakima... why not go a tad further to Leavenworth and enjoy better climbing/camping?
Thanks for the recommendations!! Middle Fork is closed for the season and Denny Campground appears to be full. I think we are going to try our luck with Tinkham (it's all walk up). And, yes, we know Leavenworth is way better!! :) We have to go into the city anyway AND we really want to clip some bolts.
Go up the dirt roads following the North Fork of the Snoqualmie. There's a ton of free camping. At least there was a decade ago when I lived in the area. I forget which exit to take to get there. Either 34 or 38. More and better camping than up Tinkham. Usually some interesting groups of locals throwing keggers in that area, but enough room for all.