I am not sure about Girdwood, I've been there, it's a beautiful and very crunchy community, but homeschooling in Alaska has a lot of support. There are many home school programs that have started up over the past 10 years or so that allow parents to enroll their children in the program to receive high quality borrowed materials and money to use for classes, travel, expendable materials, computers, etc. along with teacher "support." We used this and paid for my first two years of college (since I was also a high school student). However, if you are not comfortable with that level of control over your schooling (reporting to an office, using non-Christian materials, taking benchmark exams, etc.), currently in Alaska there is quite a bit of freedom in how homeschool families operate. There really is no agency to report to (there is, but they are so swamped they would really rather you didn't). The only tricky part would be passing the high school graduation qualifying exam (HSGQE) and receiving a high school diploma. Since I was in one of the programs when I graduated, I didn't have to worry about it (actually, the test wasn't around when I graduated 10 years ago). Anyway, I hope that helps a little bit.
We have found Alaska to be a wonderful place to learn in. Although we lack a lot of children's museums and historical sites (I grew up on the east coast where these abound), we've enjoyed experiencing life in Alaska. My parents garden, raise bees, cross country ski, have moose wandering through their yard, built their own (beautiful) log cabin, travel the state, have dog sledded, canoe, fish, hunt, etc. It is a very rich life for kids growing up, if you want it to be. You can live in a suburban neighborhood or even city (my husband and I currently live in an apartment), but it's not going to be New York City with good public transportation, close amenities (although Girdwood would probably be small enough that you might get away with walking to the corner shop), and nice sidewalks. To really enjoy Alaska, and beat the cabin fever while you're at it (besides taking Vit D), it's really best to live Alaska taking advantage of its ruggedness, etc.
Anchorage has just about everything you would need to buy. They have a Costco, a few natural grocery stores (very expensive, but they have almost everything), a few classic toys stores, two massive bookstores, and so on. They have an art museum, an indoor water park, a few native heritage exibits, several good hospitals, and a small children's science museum "The Imaginarium." There are two universities there (my husband and I graduated from UAA) and several times a year there are fun festivals, including the start of the Iditerod.
Oh, also on the natural food front, this year I participated in a CSA farm share from a Mat-su farm, have received fresh raw milk weekly (also from Mat-su), and have participated in an Azure Standard co-op out of Oregon that ships things up here on a barge for just pennies a pound. There are some good options for fresh food.
Hmm. That's all I can think of right now. I hope that helps you some!