It's a short walk to:
Scotty's Diner on the West side of Lex bet 39 & 40 makes a nice inexpensive breakfast.
If you like bagels:
Bagel Express on Lex and 40th makes a nice bagel but I prefer Ess-A-Bagel on 3rd and 50th or Vic's Bagel Bar on 3rd bet 37 and 36th
If you like Asian food there are three places we like:
Rare on Lex and 37th has great burgers, ribs etc and is a little bit fancy but not too expensive
Duke's on 3RD and 37th for down home comfort food
El Rio Grande above Duke's has some great Tex Mex