Video and photography on the campus of the US Capitol is highly restricted. It is possible to get some shots. If you are not credentialed by the radio/TV galleries you may still be able to gain access but some movements will be limited. All current policies are detailed here.

You will not be allowed to setup a tripod and shoot a standup where you would like. However, there are some good positions where you are allowed to setup sticks and get a decent shot. Inside the Russell and Canon office buildings you can setup on the third floor of their rotundas. These are the regular positions for the networks. You can ask the crews there where you can setup for a short time to get your material. See this map for the exterior locations:


Here are some photos of each of the locations inside and outside where you can do a live or recorded shot with a minimal amount of hassle.