The Catskills offer a large selection of fairly reliable ice climbs. While not quite as wintery, or scenic as the Adirondacks, and lacking multipitch climbs (except for one 6 pitch monster) this area has enough ice climbing to keep you busy for awhile. Also appealing (to some), is the fact that a lot of the ice is only a short distance from the road. Flip side of that coin though is that there's a good chance of running into a bunch of chopped up ice.
I've only climbed at two areas in the Catskills; Stony Clove & Kaaterskill Clove: Asbestos Wall.

The main climbing areas in the Catskills are:
Kaaterskill Clove, Platte Clove, and Stony Clove.

Each area has subsequent areas as well:
Kaaterskill Clove is divided between
-Asbestos Wall (very close to the road, short climbs and lots of sun)
-Buttermilk Falls (6 pitch ice climb!!!) WI3-4
-Moore's Bridge (also close to the road WI2-4+)

Platte Clove:
-Bridal Veil Falls Left (WI3-4)
-Bridal Veil Falls Right (WI2-3)
-Unnamed flow (WI4)

Stony Clove:
-East side: The Playground, Sun Wall, and Twin Columns
-West side: about 5 climbs in the WI2-3 range

Each area generally has at least a hand full of quality routes; or at least the potential for.
The climbs range from WI2-WI5 and are mostly top-rope-able.

Getting There

Take I-87 to either Exit 19 or 20, depending on which areas you want to climb at.

Red Tape

none that i know of.
parking is limited though. Especially at the main parking area for Asbestos Wall/the Ravine routes/ and Moore's Bridge: only 8-10 cars if people are nice about it.

Camping

we slept in the back of a Subaru. Lots of camping in the area; just not open in the winter. Please feel free to let me know if i'm wrong about this. It would be great to know of a place to pitch a tent.

External Links

RockandSnow.com is the local gear shop.

"An Ice Climber's Guide to the Catskill Mountains" is the book.

MountainProject.com has a lot of valuable information available. and is much more comprehensive than this in regards to route info.