What follows are a few places where I know marmots are easily seen. Plan on sitting quietly for a while to increase your chances of seeing marmots. Share with me your favorite places and I'll update the list.
Woodchucks are 'speed bumps' in many parts of rurual Pennsylvania, Ohio, and New York. Ask around and you may find fields with them living on the forest edge.
By far the best place to see marmots in the US is in Washington State. Olympic National Park (Hurricane Ridge) and Mt. Rainier National Park (Sunrise area) have heaps of Olympic and hoary marmots for your viewing pleasure.
Yellow-bellied marmots are pests at some parts of Yosemite National Park. At the Mineral King area of Sequoia National Park in California, park at your own risk for the marmots have taken a liking to brake lines and radiator hoses!
According to Karen Burgard: "Riverfront Park in downtown Spokane, Washington is a great place to watch marmots. The park was constructed in 1974 for the World Expo. It is a wonderful place with a wild river and waterfalls in the middle of downtown. At one point there was advertising for the attractions at the park (rides and IMAX theater) and the spokesmen were superheros : Captain Spokane and his sidekick Marmot Boy!"
There are a number of valleys in the alps in which marmots can easily be seen. Ask around. There is also a marmot museum which has several Eurasian species of live marmots on display as well.
The Marmot's Paradise above Montreux, Switzerland is an AMAZING place to see and learn about marmots. The displays include interative computer presentations; you can hear the alarm calls of all 14 species; and there videos, photos and a considerable amount of information about each of the species. Best of all, admission is free (you do have to pay for the cog railway ticket up).
Everest base camp on the Northern (Tibetan) side is an outstanding place to view Himalayan marmots which are (apparently) all over the place.
Khunjerab Pass (on the Pakistan-China border) is over-run with easy-to-see golden marmots. Keep your eyes open for foxes, snow leopards and wolves as well.