Check the Smithsonian web site before you go. I think most of the actual museums and the zoo are closed in the evening (budget cuts). The monuments are viewable at night, but inside exhibits (like at the Washington Monument) are usually closed.
The metro is very easy to navigate. And most locals are happy to help you figure it out. If you don't understand, just ask. They also have attendant up near the entrance of all the stations (usually in an enclosed booth).
Pentagon City is a very nice mall. When you get off the metro, just follow the signs into the mall itself. There's a place to go out to the street before you enter the mall.
Crystal City is nice during the day, but definitly empties out at night and on weekends. When I was detailed there, I was shocked at how deserted it gets, and was uncomfortable walking in the underground then.
As far as the hotel, if it's close to Foggy Bottom, you could take the metro there, but you'll probably have to transfer. I'd recommend a taxi to and from your hotel, just for simplicity since you'll have luggage. Rates are regulated, and are reasonable for a big city. Metro is great for sightseeing trips though.
Foggy Bottom metro is about 25 minutes metro ride from National as I recall. Taxi ride would vary depending on time of day. As the crow flies, it's probably 15 miles or so? As far as groceries, if you've got a kitchenette, there are probably small things for sale at the hotel. There are fewer big grocery chains in downtown, usually small convenience type stores.
Have a great trip.
