Just to throw in my two bits which will echo some of other people's thoughts and not...

Generally speaking, I think the place to stay in Vancouver is downtown'ish (ie. Bayshore) because of the higher concentration of stuff (restaurants, shopping, etc). Hilton Burnaby is about 20-30mins to downtown and you may have to fight a bit of traffic to get back. You do get a couple of malls (Metrotown and Crystal Mall) beside it. The Hilton Burnaby is newer (~<10yrs? vs the Bayshore which has been around for a while (when was it last reno'ed?)) and I would consider staying there if got a notably better rate.

I think you can fill two days worth of interesting stuff in Vancouver as you haven't mentioned some of the other "big attrations". Plus, the stuff you might want to see in Vancouver is pretty spread out so you might be spending quite a bit of time communiting.

I don't see the attraction of staying in Kamloops if you have limited time. It's a bit of drive but I'd try to make it directly to Banff.

Ditto about cutting time in Whistler if Banff is in your itinerary. I do like gglave's suggested routings thru Whistler if you want make a stop there.

During our trip a few years back (first time), we routed thru Banff, Lake Louise, Icefields, and Jasper in just a few days. We had enough time to get a taste of the parks so we weren't disappointed with the time we spent there. Didn't really feel rushed. We just didn't have a chance to do a lot of exploring.