Your best bet for staying in the city is to ride east of the Anacostia...long hills, low-ish traffic, some wide streets. I wouldn't ride out there during the week because of all the MD commuters, but on weekends it's pretty quiet (and safe). I live in Capitol Hill, so I just ride across the 11th St. bridge and I'm right there. Here's one ride that I did: http://app.strava.com/rides/20608656

Getting out of the city proper, Arlington is your best bet. Like you, I prefer to get off the trails when possible, but they're useful to get in and out of good riding areas. I usually take the Custis out to north Arlington and do loops out there. Arlington's streets are much more conducive to getting a good workout, between the hills and the much smaller number of stoplights and low traffic. There are also some good spots out in FFX if you know where to look, and it's easy to string them together into a nice, long ride. Here's one particularly long, hilly loop that covers a pretty wide array of locations out in VA:

http://app.strava.com/rides/11540525