The big trails are mainly closed in winter because nobody wants to search a rotting corpse. Smaller trails like Quarry Rock are open year around.

Hostels which sell draft beer at the places you want to hangout with. If you want to sleep quieter at night then there should be competing hostels within 1 kilometer to stay at.

If you got layers or an umbrella then go on walks along the sea wall. In January it's fine.

Then in terms of food:

• Vancouver is famous for cheap sushi. Look for AYCE Sushi chains in particular. I recommend them because I can't tell the difference between them and places that charge a small fortune.
• Try WhiteSpot. It's the local fast food chain although nowadays has been exported to Hong Kong I think.
• Chinese fusion restaurants in general. Unless you're from Asia it's probably the best place to sample Asian cuisine without going to Asia.