We are planning to take a 14 day vacation to Quebec in the beginning of July. We would like to visit Quebec City and Montreal. We would also like to stay somewhere outside of the city to do some hiking, but we are not sure which national park and area would be best to stay at. We have visited many National Parks in the United States and like hiking trails that are not super crowded and are marked.

We also love history.

Also, I have seen that there are some national holidays and the Quebec Festival in July. Will that be a problem.

Basically, we are looking for any suggestions you may have for visiting these areas.

Thanks!

The Quebec government's extensive system of parks is well described here http://www.sepaq.com/home/index.dot?language_id=1
These are "national" parks in the Quebecois phrasing. Don't worry about our enduring spats over what nations; the parks take good care of English speakers. In both Quebec City and Montreal you can enjoy long urban walks that amount to hikes. Montreal's Mont-Royal is wooded and popular, with fine vistas; the Quebec City park stretching westward from the Plains of Abraham and the Citadel (themselves run by the national government in Ottawa) are more groomed but fine for inspecting the St. Lawrence River.
Both cities are also oriented towards bicycling, by the way.
Quebec loves festivals. The beginning of July jams central Montreal for the world's biggest jazz festival and there is something being celebrated almost every summer weekend. July 1, Canada Day, brings extensive activities and fireworks to the Plains of Abraham. You can Google the official city tourism sites for both cities to get a better idea of the schedule.

Montreal and Quebec City are both fabulous. If you enjoy biking, Montreal (and the entire provence of Quebec) has some of the best road bike trails in the world. There are always festivals going on in both cities, and I believe the Montreal Jazz Fest runs into early July - lots of free outdoor concerts as well as ticketed indoor performances. As for outdoor activities, the Tadoussac area a few hours northeast of Quebec City is quite spectacular with a fjord and lots of hiking and kayaking. The Eastern Townships which is an area just north of the US border is fun to explore and is dotted with wineries, orchards, mountains, lakes, vast farms, and great bicycling.

Quebec City, so nice. I came here with my family 2 years ago. Very impressive

Thanks everyone for your responses, you were very helpful.