The White Mountains of New Hampshire offer the best hiking close to Boston, so I often go up there for day hikes. Although the Whites are not as visually spectacular as the mountain ranges of the western US and Europe, there are still some really nice hikes.
In the fall of 2000, a bunch of us went up to Baxter State Park in northern Maine to climb the state's highest peak, Katahdin, and to enjoy the fall colors.
I've been on some great hikes in the Rockies - in Yellowstone, Grand Teton, and Glacier National Parks in the US, and in Banff National Park in Canada.
The Cascade Range in the Pacific Northwest includes some famous volcanoes like Mt. St. Helens and Mt. Rainier. I've also hiked in the Glacier Peak area, just north of Seattle.
The Sierra Nevadas run along the eastern edge of California and include national parks such as Sequoia, Kings Canyon, and Yosemite.
Badlands National Park, located in the prairie lands of western South Dakota, provides lots of open space for hiking and exploring. The narrow canyons with colorfully banded sandstone walls are spectacular!
Hiking isn't the first thing that comes to mind when you think of Hawaii, but there are some really nice hikes. There is such a variety in Hawaii, ranging from shoreline hikes along the ocean to high altitude treks on the 10,000 foot plus volcanoes.