If you want to see bears in the likes of Yellowstone National Park, March, April and May are great, as are the autumn months, particularly in Alaska when they come out to catch the migratory salmon. For polar bear watching in Churchill, Canada, October and November is key time, or March when cubs come out of their dens for the first time.
For Alaska, the best times are generally mid-May until mid-September. The wildflowers are wonderful in May.
February, March and April are top times for seeing the Northern Lights up in Canada’s Yukon Territory.
Hurricanes do happen in the southern states between June and November, including Florida.
For serious hiking in the famous USA canyons such as The Grand Canyon or Bryce, the heat in July and August can be extreme and dangerously high. So, avoid the height of summer if you can, unless you are with experts. Consider visiting them in winter, when they are dusted with snow and devoid of tourists.
Public vacations are huge in the USA, so book well in advance if your vacations coincide with Independence Day (4th July), Memorial Day (last Monday in May) Labor Day (first Monday in September) or Thanksgiving (fourth Thursday in November) which are the biggies.