We've stayed at the Hilton several times and always walk to the Broadway Oyster Bar http://broadwayoysterbar.com/
we love the food and they have live music nightly. Nearby is BB's Jazz, Blues and Soup where the music may be better but we do prefer the food at BOB. http://www.bbsjazzbluessoups.com/
There's several other night spots in the S. Broadway area http://www.bealeonbroadway.com/
There's also an Imo's Pizza and a White Castle which serves as our getaway breakfast after we check out. The Hilton has a sports pub inside where most games are available.