Spring Garden Deli
As OlderPhiladelphian said, you don't want to eat there.
Two other possibilities for you:
the cafe in the Perelman Annex (across the Parkway from the main museum) is very pleasant and has good food. Cafeteria style.
Little Pete's, in the Philadelphian (entrance on Fairmount Ave) is like a diner. You can get a very decent corned beef special - or many other things.
For anything more exciting, go into town.
The name has changed and you really dont want to eat there. The deli is across the street from the gas station and it is really nothing special at all. Perhaps you were thinking of Silk city Diner at 3rd and Spring Garden and although it is something special, it is 18 blocks away. If Jewish Deli is what you want head south on 19th till you pass Market St. On your right you will see Famous Deli and you cannot do better then that in the center city area.
There is nothing that I know of that is on Spring Garden st near the Art Museum that is worth stopping at.
Market St Cafe
315 Market St, Charlestown, MD 21914
Famous 4th Street Deli (on 19th Street) is fabulous, but you will pay NY deli prices. The portions are so enormous, however, that sharing is very much an option.
If you are not looking for deli, but are ok with a "European style bar" that serves excellent food, try Bridgid's. http://www.bridgids.com/ Super beer selection as well.
There is a new place opening soon at 2319 Fairmount, called Rybread Cafe. It's owned/operated by a friend of my neice, and the menu looks promising. Here is the website. http://www.rybreadcafe.com/rybread_ca...
It was supposed to have been open by now but I think equipment delivery has held them up.