Renaissance Mayflower is a beautiful hotel. You are in a pretty good location!
I do not know your budget or what type of food your party would likes to eat, but here are some suggestions. I recommend using opentable.com to book your reservations.
Keep
TastingsJournal.com bookmarked as the guy who runs it has fab deals, usually 5-6 course meals for $45 per person. This week it's Tuscana West. I've eaten there for Valentine's Day a few years ago and it was very very pricey, so $45 is practically a steal!
GOOD AND SAFE BETS FOR LARGE GROUPS
Old Ebbitt Grill (Neighborhood: Metro Center/McPherson Sq)
675 15th Street, NW, Washington, DC 20005
Phone: 202-347-4800
Website: clydes.com
Clyde's is a local chain and they serve New American food. They own quite a few restaurants in this area. There is a location in Georgetown and also at Gallery Place/Chinatown. However their most popular place is the Old Ebbitt Grill, which most consider a DC institution. Reasonably priced, you should find something for everyone here. It gets crazy crowded at lunch, make reservations if possible.
Dino (Neighborhood: Cleveland Park)
3435 Connecticut Avenue NW
Washington DC, 20008
Phone: 202-686-2966
Online Reservations up to 10 - Private dining 11 to 60 guests
Website: dino-dc.com
Dino is near Cleveland Park and serves rustic-style Italian food. They boast a wide array of wines and run specials often. They usually have a "Restaurant Week" menu, 3 courses for $35.09. They do accommodate large parties and I once booked a room for about 8 people and they were really great with the service.
SPORTS & LOUNGE BARS
Public Bar (Neighborhood: Dupont Circle)
1214 18th St NW
(between N M St & N Connecticut Ave)
Washington, DC 20036
Website: publicbardc.com
This one just opened. I watched the NHL playoffs here. Very spacious. They didn't have a kitchen when I visited but if you want to catch a game, it is a very cool place. Three levels, large TVs. On the second level, huge booths with TVs at the booths. Even a TV in the bathroom sink. Drinks I thought were pricey but they do have a Happy Hour from 5-7 on weekdays. After the game is over it turns into an upscale place... methinks this place has an identity crisis going on.
Empress Lounge at Mandarin Oriental Hotel (Neighborhood: SW Waterfront)
1330 Maryland Ave, SW
Washington, DC 20024
Website: mandarinoriental.com/washington/
The hotel I work at

It has free jazz on Fridays and Saturdays. Very swank but we have all types of guests. Also has outdoor patio, great view of the Tidal Basin!
Please let me know your preferences and I can make better suggestions!