If you want a city as your home base, Quebec City, hands down. The old city is like visiting Europe, the Faubourg St-Jean just outside the old city walls is a great area for nightlife (including some long-established gay venues), and it's very quick and easy to get outside the city to the Laurentian Mountains, Montmorency Falls, Île d'Orléans, etc. (you could easily spend a day or more cycling or hiking around the island). It's also just a 2-hour train ride to Montréal for when you want to take the culture and nightlife up a couple of notches.

If you want mostly nature rather than a city with nature access, you could try south of Quebec City in the Eastern Townships. It's beautiful camping and hiking country around Sherbrooke.