Haha Michener is a bit outdated. Anchorage is a modern city of 300,000. Plenty of good schools and multiple modern, large, competent hospitals, costco, walmart, downtown bar scene, you name it. Although it is still only minutes from everything you inquired about, you can be in the woods in 15 minutes if you want to be. It is also a good place to be in the state geographically centralized and close to world class hiking, fishing, oceans, lakes, rivers, etc. It also and has some of the mildest winters in the state.
There are many more rural feelings areas minutes outside of Anchorage as well, such as where I live on the Knik RIver (about an hour from Anchorage). Others close to Anchorage include Eagle River, Chugiak, Girdwood, The Matanuska-Susitna Valley, and more.
Fairbanks and Juneau would be the next two options, as far as modern conveniences, but Juneua is quite isolated and way Southeast, not on the road system, and doesn't give you as much access to the rest of the state as Anchorage does. Fairbanks is in the interior, much smaller, MUCH colder, and a little boring, although would still have plenty of wilderness access.