As was already mentioned Midnight Sun is definitely worth checking out while in Anchorage. Their beers are excellent.
Anchorage Brewing produces excellent beers though I am not sure if brewery tours are possibly or not. While in Anchorage you should seek out any beers produced by Anchorage Brewing company. Their beers can often be found on tap. At the very least local bottle shops should have some of their products.
Moose's Tooth has very good pizza and is an outlet for Broken Tooth Brewing's excellent beers. Moose's Tooth is always busy regardless of the time. You should expect to wait at least 10-15 minutes but it is definitely worth the wait. My wife and I always go to Moose's Tooth at least once whenever we are in Anchorage.
Glacier Brewhouse is has very good food and beer. They are a bit more expensive but worth checking out at least once. Their oatmeal stout and bread pudding are excellent.
Snow Goose Restaurant/Sleeping Lady Brewing is worth checking out. I've heard very good things about their beers. However, I am afraid I have not actually eaten there or sampled their beers.
King Street Brewing is also in Anchorage. I've heard there beers are quite good but I do not know this first hand since I have not yet sampled any of their products.
There are two other places worth checking out while in Anchorage. Humpy's (http://humpys.com/anc
), as was already mentioned, is a good place to sample local beers. Cafe Amsterdam (http://www.cafe-amsterdam.com/am/
) is also a great place to sample beers from Alaska and elsewhere and enjoy a nice meal.
I hope this helps!