Good luck. I used to travel alone a lot. It takes some getting used-to, but can really be very enjoyable to be on your own schedule and only have to worry about your own tastes. Other than all the basics on personal security and being aware of your surroundings -
Yes, you can bring a book or magazine to a nice restaurant. Another good option is to sit at the bar if they serve the full menu there. Most nice restaurants will do that and it's not like going to a bar to "meet someone", more like sitting in a place where you've got a chance at conversation and there will likely be more people also on their own. Of course, if you want to avoid conversation, go for the table for one and a book.
Get a guide to the city before you go, so you've got some idea of places you want to visit. Museums are always good options for solo travelers. It may be too cold, but the Japanese Gardens on the UBC campus are spectacluar and another good place to walk alone. In fact, the whole campus is lovely.
Also, pick up a local paper as soon as you get there and check if there's anything culture/performance-wise you might be interested in seeing. A concert/lecture/musical/film is another good thing to do solo.
I'm not sure what sort of things you enjoy doing. Vancouver is very outdoor-oriented and has a lot of good walking and biking trails, and bicycle rentals are easy. There's also a vibrant arts scene, good shopping, and lots of good restaurants.