I haven't been inside, but I live right down the street. The hotel isn't near anything in particular, but the Metro is probably a 10 minute walk, door to door. Depending on weather, your interest in walking, etc., King Street Alexandria, where the shops, bars, and restaraunts are located, is probably another 20 minute walk past the metro - although to reach the end of the street at the river would take you closer to 45 minutes.

I can't comment on the hotel shuttle, but there is a free trolley that runs the length of King Street, so if you can get there (it ends at the King Street Metro and the river on the other end, with multiple stops all along King Street), it will take you the rest of the way down the road.

The Metro itself (Yellow Line) will run you into the heart of DC - with stops at National Airport, Pentagon City (Mall), Archives/Penn Quarter (lots of places to eat and things to see), and the Verizon Center (more shops/bars/etc.). You can easily connect to other lines to get anywhere in the metro area.

Your closest food options are a Subway on Eisenhower Ave (on the other side of the Eisenhower metro, about a block past on the left), or a little farther down, Foster's Grill (Good burgers/dogs) and a Chinese place (both on the right in a strip mall across from the Patent and Trademark Office maybe two blocks past the Subway).

There are two Residence Inns in Alexandria as well - I've stayed at one near the Federal Courthouse, which was very nice. The other one is on Duke Street, tends to be more expensive, but is much closer to the action (easily walkable to King Street). If you have specific questions, feel free to PM me.