Take a look at my Flickr page for ideas. I have a DC set. The bulk of my shots are taken in the DC area because I live in the area.
The monuments and memorials along the Mall are all good options for the 24-105. The WWII Memorial at dusk is wonderful (facing the reflecting pool and Lincoln Monument) because they light it up and it is a large, impressive memorial. I recently shot the Korean War Veterans Memorial at night, which is nice. Arlington Bridge shot in Arlington facing DC at dusk or dawn. You can shoot the sunrise and sunset from the Key Bridge, which is between Rosslyn and Georgetown. If you can do a sunrise shot, shooting from the top of the Lincoln Memorial facing out across the reflecting pool is nice. A perspective shot at the Vietnam Memorial is nice because it tapers down to a point at the horizon line and you can get the Washington Monument and reflections off the wall, all in the same shot.
I'm not sure about the telephotos. I love shooting at the National Zoo with my 70-200 (and the 135 would be nice). If you go to the zoo, be there at 8:30am to get the best shots and avoid the crowds.
If you are into plants and flowers, the National Arboretum is a nice place to go. The cherry blossom trees, which are not in bloom, are along the tidal basin. There are beautiful tulips planted there, as well as the Jefferson Memorial.