With Priceline, you can't specify the hotel you want, only the general area of the city. They are able to offer such low rates because they are just a clearing house for the hotels' excess inventories. If you want a specific hotel, you must book directly with the hotel and pay regular price.
You don't find out what hotel you are actually going to be staying at until after your non-refundable transaction has been completed. If you go to biddingfortravel.com, you can search for a specific city and find out what hotels people have been able to get at different prices. Of course, with any kind of blind bidding there are no guarantees that you will get the same deal that someone else got.
Also, Priceline can't officially be used by people outside of the US, so you have to jump through some hoops to bid as a Canadian. There is information about how to sign up for an account pretending to be an American on the biddingfortravel.com boards. The purchase and confirmation process is all done on-line, so it doesn't matter if the address in their system is false. The hotel won't care where you're from as long as your money is good (and they've already been paid in full before you arrived).
The only problem I had was trying to use my Royal Bank Visa card for payment. On the biddingfortravel.com boards, they also have reports of people being unable to use CIBC Visa cards. It is possible that Priceline has blacklisted the cards issued by the big Canadian banks. I have a CAA Mastercard issued by MBNA, and I was able to complete the transaction using that card. Apparently American Express cards work as well.