I fish the Green quite often, and though we're sort of in between runs at the moment, there are reports of early winter runs here and there.
I don't know how fammiliar you are with the area, but the best place to start(I think anyway) is Flaming Geyser State Park. You'll likely find a bit more elbow room there. Some other places to check out are Whitney Bridge Park, and Metzler Park. If you feel like driving a bit there is Kanasket-Palmer State Park just outside Maple Valley. It has absolutely gorgeous water and camping facilities which are absurdly over priced.
Then there is the Tacoma Headworks. Due to recent terrorist threats, I highly advise avoiding the place altogether. This is where we get our drinking water, and the last time I was up there the locals gave me the serious "stink eye", so I'd imagine it's a hundred times worse by now.
Next weekend I'll be up at the "Geyser" and will be fishing either a shrimpy looking purple pattern of my own creation on a sink tip, or I'll just add on a lot of tippet and fish heavy flies(Paintbrush's, G.P.'s,Comet's, ect...)on my floating line.
Remember while you're out there, that an "Any Fate But Submission" attitude will eventually land you your first fish and all that will follow.
Hope this helps,
Summer runs can sometimes be found into Dec, when the winter runs begin building. Hatchery runs show up in greater numbers first, then the natives.
I think June is when the winters are about gone and the summers are building.
Check the regs closely and watch for emergency closures.
I recommend picking a stretch of river and getting to know it really well. Watch for rolling fish and watch where others are catching fish.
If I were in your shoes and had easy access to the Green, I would probably get very familiar with Flaming Geyser or Metzler (sp?) park. Start hitting it now and use patterns that will take coho, chum, or steelies (cerise marabous for example - but lots of others). There should be some coho around (not sure though) and the chum should be building. The chum are the easiest to catch and the hardest to land. You should really give them a shot... Nice confidence builder.
metzler park is a nice place to fish i know about every hole high or low water and it also hase 1/2 mile up streem to wade and 2miles down to work if you have the gumpshon the coho are almost goen some steelys are in and some chumes they shood be geting thick now keep the sunny side up and the krusty side down keeep on trucking
Some great swing water at Whitney Bridge and all the way upstream and through Flaming Geyser Park. If you have a drift boat, raft or pontoon there is some excellent places on the Whitney Bridge to Hwy 18 section. That use to be our routine float for many years... back when I was a hardware heathen.