This is a perfectly legitimate thing to do. It's not uncommon for climbers to take a 60 or 70 meter rope and cut a few meters off the ends (since the ends of a rope take a lot of abuse). You can either take it to REI, as you suggested, and tell them you are cutting it for climbing or check out this how-to on Climbing.com.
A few things you need to consider before cutting your rope, though. If you are planning on climbing at other crags, I would check out what the height of the routes are there and make sure you'll have enough after you cut it. If you plan on climbing anywhere else in the country, I'd suggest having at least a 50m rope (and better yet, a 60m rope) to be on the safe side. I have a 70m rope and although I don't use more than maybe 50 meters of it at a time at my regular crags, it's been the difference between safely climbing a route and not when climbing at other crags. If it's a possiblity, you should look into buying a shorter rope. I say this only because I agree that it is annoying to use a rope that is on average twice the size of what you need, but nothing is more frustrating than realizing you don't have enough rope to climb a route.