Another runner briefly mentioned the Stanley Park Seawall. It deserves a better description. It's only about 10 km, so won't do for your long runs. However, for out-of-town runners, this is definitely the run to try. The park is on the edge of downtown, about 2 km from most major hotels.
Stanley Park is surrounded on 3 sides by water - with views of the downtown towers on one side, the north shore mountains across the water on another side, and the Gulf Islands on another.
The seawall is completely paved. The route skirts the water most of the way, then cuts back through the forest at the end. The loop is roughly 10 km. It is marked with brass mile and kilometre markers, with the zero point near Georgia Street, the main street into downtown. There are several water fountains on the route. There are free change rooms and showers at Brockton Oval (a running track just inside the park).
If the weather is nice, it's best to get there early in the morning before the seawall get's too busy.
Parking can be a problem when it's busy. There is usually parking available beside Brockton Oval, but if you're staying downtown the best bet is to leave your car behind and warm up with a run from your hotel along the seawalls that extend along Coal Harbour on the north side, or English Bay the south.
When you're done there are terrific coffee shops and restaurants near the Bayshore Hotel towards downtown, or along the English Bay side.
To turn it into a long run, continue out of the park on the south side - along English Bay - and cross the Burrard Street bridge. Follow the signs west to UBC. You'll be mostly along the opposite banks of English Bay and can easily do an out-and-back 20 miler along a safe, paved, scenic route.