I LOVE Quebec City and have stayed there 2 summers in the last 3 years. There is no "Downtown" per say. You the upper town and the lower town. In the lower town I suggest "Le Germain" and in the upper town I would suggest The Chateau Frontenac if you can swing it, if not Hotel Place Royal isn't a bad spot to stay in.
If you really want to save money and have an easier time parking your car, I suggest the Saint Roch neighborhood. It is about a 20 minute walk to the Chateau Frontenac (up hill) or extremely easy to visit by bus (10 min away...Bus 801 is your best friend) There is a great Best Western (about 37 USD while you are there. CRAZY GOOD) there and the neighborhood is newly gentrified with lovely shops and restaurants. One of my favorite parts of the city. There is also Hotel Pur there that is nice..
Restaurants: In the Saint-Roch area there is a great place called L'Affaire est Ketchup.
In the old part of the city there are some Quebecois chains that are excellent: Le cochin dingue, Le lapin saute, and one other. The oldest restaurant in the city, Aux Anciens Canadiens is worth a lunch stop.
To splurge, look no farther than Le Saint Amour.
Of course, maple syrup is all the rage. So is game. Take some walking tours and talk to the people . They are wonderful.
if I can help, let me know!