I transferred to Georgetown last year and I live in an apartment building called Senate Square, which is right behind Union Station. It is within walking distance to the law school and is basically brand new. It's a bit pricey, but it does allow pets. I believe you can get a 1br for somewhere in the $1700/month range right now (with specials, etc.). The rent is about the same as Mass Court, but it's quite a bit nicer. My wife and I looked at Mass Court and weren't impressed at all.