Quebec is a small enough town it doesn't really have much for public transportation but what it does have is a very well developed set of bike trails. A couple of places in the port area of the lower town rent bikes. It's an excellent way to get Montmorency Falls.
One of the things I really like about Quebec City is that there are some very nice bicycle paths. In fact, the city has used some of the money it received for its 400th aniversary celebrations to build some beautiful paths that people will be able to enjoy for many years to come. My favorite one starts near the Quebec City bridges, runs along the St. Lawrence River to the old port area, and from there continues all the way up to the Montmorency Falls. It is also possible to make a short detour to bike along the St. Charles River or take the ferry across to Lévis - the bike path on the Lévis side also runs along the St. Lawrence River, with great views of Quebec City. And these are just a few of the paths you have access to from downtown Quebec City - to see more, you can dowload a map at http://www.ville.quebec.qc.ca/fr/ma_ville/velo.shtml
Equipment: If you'd like to rent a bike, you may do so at Cyclo Services (see information below).
People in Quebec City (and Montreal) seem to be crazy about bicycling, we saw many bicylists at breakfast down in the lower town as they were coming over on the ferry from Levis and many people arriving by bicycle at the Marche de Vieux Port. I don't think we saw many people on bikes in the upper town, probably would be too crowded to ride and the streets a bit steep.