You have selected a very central hotel that will make it easy to see the downtown on foot and to have a pleasant bike ride.
Bike Ride - bring your helmets and a bike lock or two - options to rent a bike are Bixi Bike and Rent a Bike (tandems or singles for rent).
Biking - Option 1: Rideau Canal from downtown (east side) , over the locks at Carleton university and return through the arboretum and around Dows Lake takes a generous hour. Take a side tour to the Ornamental Gardens and exhibitions at the Experimental Farm if that is of interest.
Option 2: Start on Wellington street heading west at Bay street - walking on the sidewalk, as the road turns toward the Portage bridge to Gatineau, take the ramp on your right down and under the brigde, follow the pathway to the right - you will come to the Mill St. Restaurant and then turn left toward the War Museum. This path takes you behind the War Museum and then follow for a scenic ride along the Ottawa River.