There are several trails that you can hike in and around Anchorage as well as within Denali National Park, which plays host to the highest mountain in North America (Mt/ McKinley). The signs all caution you against singing or whistling too much because that tends to attract bears. We, of course, disobeyed them, but were lucky enough not to get eaten. I think the bears were still hibernating.
Kenai Peninsula: There is an amazing biomarine center that allows you to see the wildlife up close. There are also cruises you can take to get out to see glaciers and wildlife. One word of advice: take the seasick pills they offer at the beginning. They cost like a dollar or so and will be well worth it. I thought my stomach was seaworthy until it started raining and the waters get a little choppy as you head farther out.
Quick Tips:
We didn’t get a chance to take the train because it was too early in the season, but I highly recommend it. It weaves around the mountains and lakes and is possibly the most scenic route you can ever take.
The peak season is May-September, but we went in early May, when the weather was right around 40 degrees or so, perfect hiking weather and not too many people. The prices were also a lot lower than if we had gone two weeks later.
Best Way To Get Around:
We rented a car, but again, if you have time, I highly recommend the train. Anchorage is fairly pedestrian and bike friendly. There is actually a really nice trail in and around the city that loops around this gorgeous lake.