Since the weather varies so much throughout the Americas the best way to plan a trip is to first determine where you want to go, what kind of experience you want and what your budget is. That will help determine if you want to travel during off season or peak season for your destination of choice.
Winter travellers will reap the best savings in colder areas like Chicago, New York and much of Canada, the exception being ski resorts in places like Colorado or Whistler. Travellers headed south to New Orleans, Texas or SoCal, or even to Central or South America, may encounter higher prices in winter but avoid the extreme summer heat.
Summer travellers may spend a little more in areas like the National Parks, or the Canadian Rockies but the weather will be pleasant and temperate in these areas. While the heat in some areas may be off-putting, budget travellers should check out destinations like Las Vegas, Phoenix and SoCal during the summer.
Central and South America can offer great value in hotels. The flights might be long, and somewhat costly, but once you're there, food, beds and drinks will be pleasantly affordable in many places.