As with its northern neighbor, Yellowstone, the prime tourist season in Grand Teton is July and August, thanks mainly to school schedules, but the gorgeous Rocky Mountain weather is a great draw, too. Warm, sunny days followed by cool, starry nights are as much an invitation to the park as is its iconic mountain range.
True, summers can be crowded, but an easy way to find some solitude amid all the beauty is to head down a hiking trail. Cascade Canyon, which climbs up into the mountains on the far side of Jenny Lake, is perhaps the most heavily traveled trail come warm weather. But few folks seem to move on beyond Inspiration Point. If you take this trail, enjoy the view from the point and then push on further up the canyon. In places where the creek pools I've seen moose browsing for a soggy meal.
While the dry Western climate normally means there are few insects to bother you, come mid-September the early frosts will have taken care of most of any remaining pesky insects, and the cooler day-time temperatures make for ideal hiking weather.
Winter can be bone-achingly cold and snowy, but if you prepare properly the snowshoeing and cross-country skiing possibilities are spectacular. The Teton Park Road is closed to wheeled-traffic, but perfect for cross-country skiing and snowshoeing, and if you want to mix a little alpine skiing in there's Jackson Hole Mountain Resort and Snow King in the neighborhood.
During the winter months rangers lead guided snowshoe hikes from the Craig Thomas Discovery and Visitor Center. When the snow starts to fly and you find yourself in Jackson, call 307-739-3399 for details and, if necessary, reservations. Yet another great way to enjoy Grand Teton during the winter months is to plan a side trip to the National Elk Refuge, which offers sleigh rides across the refuge grounds as early as December, snowfall permitting.