i see the delta as the host hotel for the race. it is pretty close to the site, although if you look in chinatown, I've heard the holiday inn there is decently priced. (there's a convention center next door so they have a lot of traffic)
http://www.velo.qc.ca/...nts/rvm-montreal.pdf if you look at the map, the race is near the bottom right, near the "112" sign. (the little island) anyway that's the main bike path to get to the island (unless you take our infamous metro) the hotel is barely 10min bike ride away. (near that 720 sign but even closer to the race site)
I live here so I really can't say where's cheap but if you look online, I think old-montreal (vieux-port) is probably the closest to the site (close enough that you will be able to bike there; warm-up). Downtown & chinatown are close too but if you're not used to riding in traffic, Montreal is not the place to learn (we drive like maniacs). And the metro (subway) is always cheap and efficient too.
http://www.stcum.qc.ca/English/a-somm.htm (ps. old montreal is a great place to stay as well, you'll have plenty of things to do)