I have a sister who lives in DC and getting around should be easy. Every location can be reached by going down Glebe, turn left at the brick colonial town house, and then turn right at the brick colonial house. That's the way it seemed to me anyway. Riding a bike is the best way to get to know a place, it just takes a little time. Places settled in early Colonial times have many roads that were originally plotted by deer and cattle. So I can see why the East Coast can baffle people who are used to north-south and east-west grid system with a few diagonal streets like Chicago.
Be carefull with the DC weather. Although it will be mild compared to Chicago, the damp cold can really penetrate... right into your bones. After 30 minutes of riding, I think sweating will start to be a factor. Probably would be worth it for you to invest in a good Gortex jacket.