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.
Befriend your hotel's conceirge. Solo travellers can be directed to a lot of enjoyable activities, with the added benefit of an 'insider' who can steer you clear of tourist-trappy things or wandering unbeknownst into unsafe neighborhoods on foot.....
I agree with all the above advice. I have a note book of places I want to see other wise I tend to waste time.
I usually eat in the hotel at night when I am away on my own. Day time I eat out. I never say I am on my own. I know most cities are safe, but just my extra security.
I carry a purse that is large enough to tuck my book into so I don't have to walk into the restaurant carrying it. I also ask for a booth or table that is not in the center of the room so I am not stuck out in the middle of the room with everyone walking by me while I read (though I also won't take a horrible table such as by the kitchen just because I am alone).
Whenever I am in my hotel room I keep the bar lock flipped over for added safety. Also ask for a room that is near the elevators but not right next to them so you don't have to walk down a long hall way at night.
I agree with eating in the bar as it always provides a place for conversation if you want it. And like Chris says be careful at night. If you do go out to eat then either take a cab or if you have a car valet park. I cannot stress the importance of your safety.
When in doubt ask to be walked to your room or car. Security is always willing to do it. Don't feel like you are being paranoid. Trust your gut it won't steer you wrong.
Have fun some of the most enjoyable trip I have taken have been on my own for business and pleasure.
The West End of Vancouver is safe enough at night to go out and eat. I live there alone for a year and never felt threatened. (Never advertised that I lived alone). The West End has a high population of gay men. I'm not sure if that's what made it feel safe to me, but it was a very nice place to live.
As long as you don't do something stupid like go into Stanley Park alone at night, you should be fine.