embdts,
There is only one local organized climbing group, and that's the
New York/North Jersey Chapter of the AMC. You haven't mentioned anything about your experience level but if you are a beginner they do offer a pretty good and modestly priced four day beginner program each spring. If you don't want to wait until next spring, the various local guide services are your best bet for beginner climbers at the Gunks.
If you have some experience, hang out at the Mountain Deli, at the intersection of 44/55 and 299 in Gardiner, very near the base of the cliff. Weekends it tends to be busy and many passing through the deli are from out of town and often on a mission with a specific partner or group of friends. During the week it's quieter, more laid back, and easier to strike up a conversation.
On a different track, many of the out of town climbers are tight with each other,and strong, because they develop friendships at climbing gyms. The Gravity Vault in Upper Saddle River, NJ, and The Cliffs in Valhalla, NY, are about equidistant from Fishkill at 50-55 minutes if pulling plastic some of the time appeals to you.
Also, you might want to go to the Tom Spiegler benefit golf tournament that Ranger Rob is organizing. It's for a good cause and you'll likely meet many other climbers. Info can be found elsewhere on this website.
Lastly, Bacchus, in New Paltz, is sort of the Gunk's climber's version of Cheers. If you're the gregarious drunken type it's a good place to meet other gregarious drunken climbers.
Best of luck to you and welcome to the neighborhood.
Kent