There is bouldering as (briefly) detailed in the excellent boulder Britain guide (which is excellent).
Main options:
1) Peel - sea washed frictionless-ish red sandstone. From the Skate park end of the prom head up over the headland and down to the next bay (where there are the remains of an old outdoor swimming pool). The bouldering is based around a cave and arch to the right (north) of this. Good venue but fickle conditions (I don't think I've ever seen it dry over christmas there) and from time to time all the pebbles get washed away by the tide leaving death on a stick landings.
2) Laxey - the topo on Vimeo tells all
3) The Chasms - there is a small buttress at the top of the chasms that has several boulder problems. Those of any difficulty are eliminates. There is also a training traverse a bit further down which is about fr7b, I couldn't describe where it is in any meaningful way as the area is a bit of a maze.
There are a couple of other spots which are either dirty, unlikely to be dry, hard to find or all of the above.
There is an indoor wall under construction, it is on the industrial estate behind the power station in Douglas. I don't know if it is climbable yet??
Doug Hall lives over there and is always keen to get out climbing. He's probably the islands only properly keen climber although there are a couple of other guys who at various time get out a bit and there are lots (i.e. several, it's a small place) of people who are "climbers" that have never been seen climbing anywhere on the island. Anyway I can give you Dougs number if you PM me and he'll meet up and show you the sights happily I'd imagine (if he's not buggered off to warmer climes for the winter). I'd say you will definitely need a bouldering mat as the landings are unfriendly generally (although the stuff at the Chasms would be OK without) and if you have a hankering for adventure style trad then stick the rack in too. I've never climbed at Gogarth (I know, the shame) but I suspect the Isle of Man is a bit like Gogarth turned up to 11, so the Llyen I guess??
There is a sport crag there but the approach is epic and I doubt that conditions would be much fun in the midst of Decemeber.
Top Tip is get in touch with Doug. If he's there you couldn't have a better guide, PM me for his number.
Hope that's helpful. I'm normally over at christmas so would have been happy to show you round but this year I'm at home. However I go over quite regularly (in-laws innit?) so give me a shout if you're heading over again and should the stars align and the fates allow I may be able to offer a tour.
The other possible source of info is JKarran on the other channel, he lives over here now but is from the IOM so may well be heading back that way for the festive period, might be worth looking up his UKC profile and wanging him an email?
Hope that helps, if you have any other questions I'll try to answer them.
Nik
P.S. Everybody on the Isle of Man appears to be alcoholic, not relevant to the climbing, just a general observation.