Hello, check out translink.ca and look for the cycling route map. Tis a great system. Vancouver area is relatively flat with some hills.
As for theft, I had a relatively old xs mountain bike stolen years ago at emily carr while I was in class for a few hours and had locked in what I thought was a safe area. I know I forgot my D lock that day but...the police eventually found it at a nasty pawn shop and I had a few more years with my precious specialized hardrock, but it had suffered some damage. Bikes are stolen all the time. Know your bike's serial number and honestly, the police will look for it! I think bikesnob has some video about how to lock your bike. Lock frame, wheels, saddle with Ulocks, chain locks etc.. My husband is too nervous about bringing bikes into Vancouver so we rarely do(which sucks because I love biking in Vancouver and hate bussing it), but I have come in with my surly and locked it up best I could and was still there, but did not leave outside overnight. I'd even be nervous about leaving my 'beater' bike alone.
Which hostel are you staying in? The offical HI's should have a place for bikes(and lock them inside too), you'd be surprised how many hotels have bike rooms. The Sylvia has one and I usually stay at the Victorian Hotel which has space in the basement. It's a totally affordable full of antiques and beautiful rooms hotel and is very central. For 2 people it is less expensive than hostel.