The Julien Inn is downtown and is beautifully redesigned, don't know the price. Fine dining at Pepper Sprout or Woodfire Grille, Vinny Vanucchi's if you like Italian, Crust if you like pizza, Tony Roma's offers outdoor dining overlooking the river, Catfish Charlie's for seafood lovers. If you like wine and a good singer, go to Stone Cliff Winery on the river with Johnnie Walker on Friday night. Friday night is also "All that Jazz" at the Town Clock Plaza, music and eats/drinks. Don't miss the National Mississippi River Museum and IMAX theater. Diamond Jo Casino and Mystique Casino/Dog Track if you're gamblers. Most of this is all within walking distance of either downtown hotel. If you want to stay an additional night, Peter Frampton plays at the Mississippi Moon Bar at the Diamond Jo, along with the guitarist from Toto and Rick Derringer at 8:00 Saturday night. Good luck and enjoy Dubuque! (Galena is great for shopping, snacking, and drinking...many good restaurants there, too!)
Sorry, this was much more than just ONE "must do".