jessica,
July will likely be a busy time for hotels in all the areas you mentioned, especially in places like Whistler. It may be possible to get a room "on the fly" but it would be better (IMO) to work out an Itinerary and book ahead. That way you don't have to waste time looking for hotels when you arrive in a particular city, and can devote your time to sightseeing.
I assume you're renting a car when you arrive in Vancouver? If the hotel you booked is in the main downtown area, you'll likely be paying for parking during your stay.
With only a very short 10 nights, you'll need to prioritize and limit the number of places you visit. One possible Itinerary.....
- 3 nights in Vancouver. Have you decided which sights you want to see in that area? I'd suggest using public transit there as much as possible, as traffic can be terrible!
- 3 nights in Whistler. Hotels tend to be rather posh, so be sure to budget accordingly. On the way to Whistler, you might stop at the Sea To Sky Gondola for some great views. There will be music concerts at the top on some days. There's also the Peak To Peak gondola in Whistler (assuming you're not afraid of heights). There are lots of hiking opportunities in the Whistler area, but I would suggest contacting a local firm for advice on which places are best to hike, as there are some caveats to be aware of.
- drive back to Horseshoe Bay and take the Ferry from Nanaimo, and the drive to Victoria for 3 nights. That trip will take the better part of a day. Have you researched which sights you want to see in the Victoria area?
The Sunshine Coast is also an option, but travel times will be longer as you'll have to take two Ferries if you intend to go all the way up the coast. Keep in mind that queues at the Ferries will be longer in the summer tourist season, so getting reservations on the Ferries would probably be a good idea.