There are a number of very good inexpensive (mostly Chinese) and moderately-priced (mostly ethnic) restaurants in the area surrounding the MCI Center. Here are the ones that I have patronized and can recommend, with links to reviews from the Washingtonian Magazine for further information.
CHINESE
Since the MCI Center is in Chinatown, there are some good Chinese restaurants in the area. They are:
Tony Cheng's Seafood Restaurant - Although they specialize in seafood, there are also good pork, chicken and beef dishes here as well. However, if you don't mind seeing your food alive before you eat it, I would order something from the large water tanks in the dining area, if you see something that strikes your fancy. I have had, and enjoyed, the szechuan shrimp balls, and the fresh dungeness crabs and lobster.
http://www.washingtonian.com/dining/restaurantDetail.asp?id=1142 Full Kee - The things to order here are the meal-in-a-bowl soups, such as the shrimp dumpling soup with or without noodles and the Cantonese roasted meats (pork, chicken or duck). A delicious and satisfying meal for two might include two bowls of soup, an order of bok choy (Chinese broccoli) and an order of roasted pork or poultry if you're really hungry.
http://www.washingtonian.com/dining/restaurantDetail.asp?id=74 Eat First - The soups here are also good, though not, I think, as good as those at Full Kee. Very good roasted meats and other Cantonese specialties.
http://www.washingtonian.com/dining/restaurantDetail.asp?id=1769 Lei Garden - The General Tso's chicken is very good.
http://www.washingtonian.com/dining/restaurantDetail.asp?id=1741 ETHNIC
Jaleo - This restaurant specializes in Spanish tapas. Tapas are appetizer-sized portions of various Spanish dishes, and they are done very well here. Especially good are the garlic shrimp and the omelette with potatoes and onions. Depending on how hungry you are, count on ordering two to four dishes per person. Excellent freshly baked bread and very good sangria.
http://www.washingtonian.com/dining/restaurantDetail.asp?id=104 Cafe Atlantico and Andale - Very good Mexican (Andale) and Latin American (Cafe Atlantico) food. At Andale, try the leg of lamb.
http://www.washingtonian.com/dining/restaurantDetail.asp?id=1775 http://www.washingtonian.com/dining/restaurantDetail.asp?id=244 BARBEQUE
Capital Q - Very good Texas-style barbeque, which, of course, means a tomato-based sauce, and not the vinegary sauce associated with North Carolina 'Que. The beef brisket and pork ribs are especially good, as is the jalapeno cornbread.
http://www.washingtonian.com/dining/restaurantDetail.asp?id=1213 A word about price. Moderate, in this area, means that a three corse meal plus drinks will cost you from $50 to $75 for two people. At the Chinese places and Capital Q, you should be able to easily get by for less than $50. Also, try to eat before 7 o'clock. After that time, you're liable to have to wait for a table, especially on weekends and especially at the ethnic restaurants. For some reason, they tend to be more crowded than the Chinese places, perhaps because there are more Chinese restaurants in the area to choose from. Let us know where you ended up going and how it was. Bon appetit!