Near the Convention Center is tough. Convention center areas usually appeal to the tourists that come to town as conventioneers. Therefore, you are far more likely to be within walking distance of a Bubba Gump Shrimp Company or Phillips Seafood than you would be decent pit beef.
That said, the MOST convenient, within walking distance, comes with an asterisk....well, two asterisks. The first, is that the beef is ordinary; the second is that you must purchase a ticket to the Orioles game to get to Boog (Powell)'s Barbecue
. I think the sandwiches still run around $10, but if you can score a ticket cheaply on StubHub or a bleacher at game time, it would definitely scratch your itch.
The next place that is within walking distance also comes with an asterisk - it is only open on Sundays. There is a stand in the Baltimore Farmer's Market
- Beef Barons - that makes a more than respectable pit beef sandwich. When I was last there about two years ago, the sandwich ran about $6, had a good, smoky flavor and was quite filling.
Chap's is not walkable, nor is Pioneer Pit Beef (which I prefer to Chap's), but both are accessible by public transit, which would take 30 (Chap's) to 45 (Pioneer) minutes each way.