[Kims Robot]

I would start by taking a look at some of the Hall of Fame Teams

I'm probably paraphrasing too much, but just from memory some innovative things that stood out to me:
1114 - Big Simbot/Little Simbot, App, Kitbot on Steroids
359 - Founded Hawaii Robotics (first statewide govt level commitment if I remember right), Traveled to Japan/Guam/Philippines
341 - Team in a Box, Girls in Gear, Singapore/UK demos
236 - WDC Trip to talk to Congress, Alumni Involvement
842 - Produced Video shown in Movie Theaters, Readers Digest, Sponsor Underwater Robotics Competition
365 - MOE University, MORE Literacy Program, FLL/FVC Tracking
111 - City Tye-Dye day, Govt involvement, Strong Partnership/Alumni Involvement
Etc...

You can also look at many of the RCA winners for what they have done, there are plenty of up and coming teams that have strong programs as well!

The biggest thing is to try and come up with something that is Unique about your team, and that can set you apart from other teams. Some program or way to spread the message that no one else is doing (which is getting harder and harder every year!), and FOCUS on that. Everyone does FLL/FTC/Vex/demos/community service, but what do YOU do that is different?