We've been to Quebec City many times (most recently earlier this year). We have stayed in several locations. If it is your first visit, I would suggest trying to stay in Old Quebec in the Upper Town ("Haute Ville"). That said, there are many nice hotels in the Lower Town (Basse Ville). As the previous poster commented, it depends on your level of fitness. I think going from the Lower Town to the Upper is not that big of a deal, but if walking up a hill for 5-10 minutes is challenging, then keep that in mind.
One of our favorite hotels is the Hotel du Vieux Quebec, which I think is in an ideal location (in the Upper Town). They bring you breakfast every morning, then hang it on your door in a little picnic basket - fresh pastries, juice, etc. Depending on your specific dates, I suspect it is probably $250-300 per night.
QC is one of my favorite places. Please feel free to direct message me with any other questions!