Man, what a loaded question. I can see both of the teams I work with going to multiple offseason events in their respective areas. I know 422 went to Battle o Baltimore and the Richmond Rumble last offseason, and they want to add on BattleCry, Ramp Riot, Duel on the Delaware, CORI, and maybe IROC. You guys could go to IROC, like Ryan said, but the Rumble and the Battle are also local options.
Offseasons are great because they generate interest among students about the team (I love them because I finally can go to a robotics competition and be stress-free
). Build your team around some offseasons as if they are your regionals to mobilize your team more often.
A good thing to have soon would be an end of season review to discuss successes and shortcomings on the field, in the pits, in the shop... every facet of the team. Take time to make a detailed business plan that budgets money, outlines the team's mission and vision, and sets specific short and long term goals to give the team direction.
Talk to local teams about how they build their robot and figure out if you want to improve your machining capabilities. Think about setting up a permanent, semi-independent outreach division that makes the team a positive force in the community. Both of those require money, so identify potential local corporate sponsors your team could add to improve your revenue stream and provide greater possibilities for your team, its members, and community members. You have three specific teams I can think of within a 30 minute (traffic free in Northern VA, heh) drive that you could probably get in contact with: 1885, 116, and 612 are teams that could help you with outreach, machining, and fundraising respectively. You can also get in contact with one of the many overactive students on 422 who run the necessary subdivisions of operations and technical programs on the team.
Most importantly, go show people your robot! You guys built a pretty solid piece of machinery, so go show it off to your school and sponsors, go to community events, and get your name and FIRST's name out there!