Go check out the crit at Seward Park tomorrow night. I think there are only a couple more left this year before the series ends. You're also really close to I-90 which will get you to a terrific loop around Mercer Island. Just head across the I-90 bike path (entrance is from corner of Lake Washington Blvd S and South Irving St, right above the freeway). Once you get to the other side of the bike path, you'll empty out on West Mercer Way - either turn right and go counterclockwise around the island or go straight and follow the bike path until you reach the other side of the island, then turn right on East Mercer Way and go clockwise. East Mercer and West Mercer are the same road, just on different sides of the island. It's a really good route with reasonably polite/light traffic, good pavement, very few stops.
Even if you're not interested in racing, you can still join one of the many local racing teams, all of which are having "Meet The Team" rides starting now. Here's a calendar of which teams are riding when: http://www.wsbaracing.org/meet-the-team-rides.html
Some of the teams do really good Development programs - meaning they have good organization in place to mentor new riders/racers. One of those development-oriented teams is Union Bay Cycling. They do several specific things throughout the training season that are geared toward making newer riders more comfortable in a pack, and teaching them sound fundamentals of racing and training. Incidentally, you don't have to wait for the UBC Meet The Team ride - if you think you're interested, you can join the team ride on sundays, which leaves from the intersection of 25th Ave NE and the Burke Gilman Trail (next to the Silver Cloud Inn on 25th NE). This is right near U Village shopping center in the U District. The ride meets at 9am and will typically, during this time of year, be a 2hr endurance-paced ride.