Spoke and Sprocket in University Place (near Fircrest Golf Course) does some semi-hammer rides on Saturday mornings at 8 am and also does some wednesday evening rides. Depends on the makeup of the riders as to the speed, but usually 20-22 mph in the flats.
Tacoma Bike (new bike shop just off Puyallup Ave) does some rides I've heard are pretty fast on Sundays, check with the shop for times and start locations.
Old Town--in the offseason does rides on Saturdays in the am from cutters point coffee on 6th Ave.
Rainier cycle--no rides I'm aware of.
Tacoma Wheelmen rides are at a very sedate pace with lots of coffee stops.
Toughest group ride that I have done in the south sound is with the Capitol Bike Club in Olympia, last summer I went on a couple of crowded group rides 30-40 riders, that reached speeds in the mid and (sometimes) upper twenties with constant accelaerations and attacks. I was dropped numerous times--I don't race, and riding with that crew I realized I was nowhere ready to race.