Most places very close by are quite pricey, high-end steakhouses and such. Some budget options:
Parish Cafe -- casual bar/restaurant with excellent sandwiches.
Jacob Wirth -- cool old tavern, great beer selection, decent American pub food. Skip the German food.
Mon Tien -- very good Thai place. Thai specialties menu is less Westernized that the regular one.
Xinh Xinh -- excellent Vietnamese restaurant in Chinatown, easy walk.
Vlora -- Albanian/Greek/Italian, cool-looking basement space, reasonable prices for fine dining.
Silvertone -- hopping basement bar with good drinks and terrific, casual American food. Great values on the wine list, too.
re: MC Slim JB
Going along with MC Slim here, Chinatown is about a 10 minute walk from Park Plaza, and people often dine solo in C-town. Search for threads on this board for recommendations in that area.
And as for "Skip the German food" at Jacob Wirth's, I have to go on record again and say they do a darn good Schnitzel, especially the Jaeger Schnitzel!
Across the street is Davios. You can sit at the bar and the bar menu is reasonable. You can also sit at the table in front of kitchen-solo-has some good action. Also, Pigalle has a great inexpensive bar menu but only has 5 seats. Hint go real early or after 8 when people leave for the shows.