We visited QC for 4 nights back in August. Stayed at Le Château Frontenac which was interesting. Very touristy but great location right on the promenade overlooking the river.
Take the funicular down to the old historic district (or take the stairs) where there are tons of shops and restaurants. Very European feel. Just enjoyed walking around that area, the promenade, and the neighborhood surrounding the hotel. Drank a lot of beer and liked a microbrewery called La Barberie the best.
The waterfall DiV referenced is Montmorency Falls and they are a short drive out of the city (20min?). Beautiful scenery and there’s a zip line and cable car that you can ride to take it all in with a great view. Don’t know if that will be up and running in February though 🥶.
Directly across from the falls via a bridge is Île d'Orléans. Small island that was one of the first places to be colonized by the French. Felt like stepping back in time as I believe many families have stayed there throughout the generations. A lot of wineries, cheese shops, farmstands…we just drove the circular loop around the island after visiting the falls, enjoying the scenery. But again, things might not be so open in February.
One last thing: Poutine