I know for a fact there are a few hot rod/car clubs down in Tacoma, but I forget the names. I am a motorcycle club guy myself! (Brit Iron Rebels) A Club called the Mischief Makers sponsors Hot Rod a Rama in Tacoma in the area of the Swiss Tavern in August. Don't let the Tavern throw you, it takes up several blocks and 90% of it is accessible to under 21 folks. I plan on taking my 14 year old son. They didn't do it last year, but I went the year before, it was a blast. Loads of cool cars and trucks, all pre '65, no trailer queens and a build it yourself vibe vs. Microsoft exec-rich-guy who-bought-a-hot rod-vibe...They should have some pretty good rockabilly bands as well, maybe a pin up show. A couple of good vendors, last time there was a pinstriper working on scene...Heres a link
http://hotrodarama.com/about.htmlI am not associated in any way....
As far as Clubs in general, I can say that being in my motorcycle club has made the whole experience 100% better. Riding is fun to begin with but the addition of good friends and a collective knowledge of bikes and mechanics, not to mention places to ride to has been in valuable...If you can find the right Club, go for it!