Long time, first time ...
Darwin's is a legendary downtown bar, a favorite among sports journalists in the city for decades. If you're looking for a place to park it and drink until you can't drink no more, this is a good place to go. A real pro's bar.
The Polar Bar, a little east of the downtown hub, is another great dive bar, a place to just get wrecked. Crossroads is also popular with the local newspaper set because of its proximity to Sullivan Arena.
F Street is a nice, low-key bar with pretty good food. Humpy's Great Alaskan Alehouse, also downtown, is another place with good food and an awesome beer selection. It usually has live entertainment of some sort.
Moose's Tooth has great pizza and another impressive beer selection. Blues Central makes great French dips and has live music every night.
Chilkoot Charlie's is the main meat market in Anchorage. It has its charm, I suppose, and is routinely voted the city's best bar. It's also the bar you will most likely be killed by aggressive bouncers. (Crossroads is where you'll most likely be shot in the back of the head while sitting at the bar.)
The Pioneer Bar has become a bit of a haven for douchebags. The Avenue recently underwent a face lift and is a good place to hang out with a group.
Hope this helps. At this time of year there are only a few things you can do in Alaska, and drinking is one of them. We've been well below zero for a couple of weeks now, but it's supposed to "warm up" in the next couple of days, which probably means more snow.