Romantic dinner for 2 near the Renaissance (State & Wacker)?
I really like Catch 35, 35 West Wacker Drive, for a cozy seafood dinner (they also have a killer filet mignon). http://www.catch35.com/chicago-01-home.html. You could throw a rock from the front doors of your hotel and hit it.
Bin 36 is great, 339 North Dearborn, as is their other restaurant, A Mano Trattoria, which is underneath it (a bit more scaled down than Bin 36 but still nice). http://www.bin36.com/index.php
There's Petterino's, 150 No. Dearborn, which caters to the theater crowd, so call ahead to make sure you arrive after they scram (it's crazy before a show but quite nice when it sort of clears out). http://www.petterinos.com/
Keefer's, 20 West Kinzie, is a few blocks away, and a lovely place to dine. http://keefersrestaurant.com/
Also very close to the hotel you have the chains: McCormick & Schmick's at 1 East Wacker Drive for seafood, or Smith & Wollensky (steak) across the river at 318 North State. Sullivan's Steakhouse is probably the farthest away at 415 No. Dearborn (just a tiny cab ride if you think you don't want to walk it).
Of all these selections, I think either A Mano or Bin 36 would be the low-key-est, but nice enough for an enjoyable dinner.
Don't let anyone talk you into Fulton's on the River.