I used to live there as well (in Issaquah) and I know of two campings near Seattle
There is one in Kent in the valley just south of where I-405 runs into I-5.
- Seattle/Tacoma KOA 800 562-1892
There is another one in Issaquah just off of I-95 and the junction of Front street.
- Issaquah Village RV park 800 258-9233. This one gives you a straight shot into Seattle going down I-95
This is about as close as you are going to get to down town Seattle.