There isn't much singletrack in Carmel Valley, actually there isn't much in Carmel Valley other than golf courses, a couple vinyards, some horses, and some overpriced boutique-type shops with a bunch of crap in them.
That said, there is some great riding with quality trails within 10 miles of Carmel Valley Ranch: the old Ft. Ord (location of the Sea Otter Classic
a link to a great trail map. There are more than 60 miles of trails most of it singletrack. The easiest way to get there is to take Laureles Grade Rd. (bottom center of trailmap) from Carmel Valley Rd. over to Rt. 68. This road goes over a pretty big ridge so I wouldn't recommend riding to Ord from Carmel Valley Ranch. I recommend parking at the Creekside Terrace Trailhead (on the right side of the trail map) because that is the closest trailhead to most of the best trails. If you'd like specific route recommendations, let me know what you are looking for (time and distance), the types of trails you'd like, and skill level and I'll hook you up. I'd take you out myself, but I'm moving to VA in June. If you don't mind driving farther than 10 miles or so, there is also some great riding up in Santa Cruz - about an hour north.
As far as a rental - best bet is to try these shops:
Jocelyn's Bikes (downtown Monterey) - (831) 649-8520 **great shop**
Aquarian Bikes (downtown Monterey) - (831) 375-2144 another good shop
Bay Bikes (on Cannery Row, Monterey) - (831) 646-9090 they do rent bikes, but not sure how trailworthy
Carmel Bicycle (on Carmel Valley Rd ~5mi west of CVR) - (831) 625-2211 doubt they rent, but could help you with info on singletrack in Carmel Valley itself.
If you're staying at Carmel Valley Ranch and you play golf - try to get a round in on the course - it's a pretty good one. Though if the choice is ride or swing at a little ball, definitely go for the ride. If you'd like some pics of the riding at Ord, I can link you to some. I don't have many because I'm usually too busy riding to take any pictures.