I have a fair bit of experience with Alyeska as I lived out there for a winter.
Nice mountain. Terrain wise, the mid section is one giant bowl with the typical features (a few cruisers, some ungroomed areas left for bump, etc) carved out of it. The lower area has a few nice groomers. The best terrain is off the North side of the mountain. The top is nice and steep coming out of the chutes, or, if chutes aren't your thing, you can enter near the tram and access the lower 2/3. It's nice terrain, steep...rolling, variety of little micro-areas.
The unbeatable part is the view. On a clear day the view from the top over Turnagain is absolutely incredible. There aren't many places in the world this beautiful. If you have a day off, driving along the Seward highway is a real treat. Honestly, probably the most stretch of highway in the country. I drove it a lot when I went back and forth from Girdwood to Anchorage and it's spectacular. Heading out to the Glacier about 10mi South is quite beautiful as well. I never made the trek over to Valdez as the road was never open when I had a chance, but it's supposedly beautiful as well. The drive to Seward is equally as stunning.
The real gem of the area in terms of skiing, though, is the backcountry. When I was out there I didn't know anyone yet and had little experience backcountry skiing so I wasn't comfortable going out on my own. Had I had the money, I would have definitely gone out with Chugach Powder Guides. They run a heli and couple of cats into the area and it's supposed to be outrageously good skiing. (I dearly regret not going and will, without fail, be going back out there at some point for a purely backcountry trip).
January is a COLD month. Temps can routinely be a high of 0 to -15, so be prepared. Also, the area is a bit short on daylight that time of year. Sunrise will be around 9 or 10am and set around 3 or so (depends on what time in Feb).
Girdwood is a tiny little mountain town with some of the friendliest people I've ever met. For ski gear, DEFINITELY use World Cup in the town of Girdwood. They're great people, and very knowledgable. You can pick their brains for all sorts of info about the area.
There used to be a bar in Girdwood called Max's that was a fun place to hang out, but they may have closed down and turned into some sort of upscale bistro that doesn't really fit the area...oh well.
In Anchorage, the Beartooth is a great restraunt/beerpub and also has a movie house that serves food and beer as well. The Moose's Tooth is owned by the same people and has great pizza and beer. Try Gwennie's for a good, uber-fattening breakfast and bloody mary...it's scuzzy, but it's oh so Anchorage...
Downtown Anchorage isn't all the much to write home about. It makes for a couple of hours bumming around if you're short on things to do.
For good advice on outdoor stuff to do, don't hesitate to drop by REI. I worked there so I can vouch for the fact that 95% of the people that work there really know their stuff, are very friendly, and can give you great ideas of where to head into the backcountry if you're interested.
If you've never been out there, I strongly urge you to grab a car and drive out to see some good views of Denali on the Parks highway (stop in Talkeetna at the Roadhouse for a great lunch before you turn around). Talkeetna is the town they based Northern Exposure off of. Make sure you go on a clear day, though, as Denali is often absent if it's a bit cloudy.
You can also drive out to Hatcher's Pass (about an hour or so from Anchorage) for great snowshoeing and views of the Talkeetna's.
In Anchorage, there's good snowshoeing and x-country skiing in Kincaid park. On snowshoes you can get off trail and make it down to the ocean where you get a clear view of Susitna and the opening of Turnagain arm.
Let me know if you have other questions,