Summer travel in the U.S. generally takes place from May to October, although it is possible to travel year-round in most American states.
Here is a guide to what clothing to pack:
Socks and underwear
You might want to pack one or two pairs of warm wool socks, especially in May-June and September-October. They may also come in handy in July and August if you plan to do water sports or if your feet tend to get cold at night.
Shoes and sandals
You will need a good pair of walking shoes, both in town and for exploring the great outdoors. Everyone walks a lot while on holiday. It is a good idea to have 2 pairs of shoes in case it rains. You will also appreciate sandals in July and August.
Bring light clothing (shorts, T-shirt, tank top,...) in July and August, and for warm days in June and September.
You will need some warmer clothing (jeans, pants, long-sleeved shirts, sweatshirts,...) throughout the summer. Evenings can be quite cool even in July and August. Also good for layering. You might want to bring something a little more fancy for restaurants or other social outings.
Always pack a polar fleece (or wool) sweater, at any time of the year.
A raincoat or rain jacket is always handy for rainy days. A breathable rain jacket (e.g. Gore-Tex) over a sweater is a winning combination for colder nights.
A brimmed hat is highly recommended for protection from the sun. It might be a good idea to pack a warm hat (tuque) for cooler weather (or ocean / mountain excursions): remember, you lose 70% of your body heat through your head. A light scarf could also be useful.
Swimsuit and pyjamas
Don't forget your swimsuit for the beach, the pool and water sports!