Map from Google - United_States

The United States is a huge country, therefore it has a considerable climatic variety. In general, however, it has a continental climate, with cold winters (often frigid) and hot summers (sometimes very hot), more or less continental depending on latitude and distance from the sea. There are, however, some exceptions: the west coast on the Pacific Oceans is cool and damp in the north and Mediterranean in the south, the coast of the Gulf of Mexico is mild in winter and hot and muggy in summer, Florida is almost tropical, the mountainous areas are cold in winter and cool or still cold in summer, and finally the deserts, which are mild in winter and torrid in summer.
Since there are no obstacles to the descent of cold air from Canada, almost all the country can experience sudden cold waves in winter, but they have different durations depending on area: they last a few days in the south, lowering the temperature a few degrees below freezing (0 °C or 32 °F) in mid-winter, while they are intense in inland areas, in the highlands and in the north-east. Even the summer heat waves can be intense, especially in inland areas. In general, the western half of the country is more arid than the east, with the exception of the north and central coast of the Pacific.

United States: west and center-east

See the climate of:
United States West
United States Centre East

It's hard to find a single period which is best for the whole country. In general, however, since the climate of most of the United States is cold in winter and hot in summer, you can choose spring and autumn. It must be said, however, that in spring tornadoes are possible in east-central inland areas, and in autumn hurricanes can affect the southern area.

The west coast, including Seattle and San Francisco, being mild in summer, can be visited from May to September. The coast of Southern California and Los Angeles can be visited throughout the year, but it is preferable in spring, from March to May, so you can move to the interior of California without fear of the heat (but in the desert the month of May can be already hot), or to the parks of the Sierra Nevada without fear of the winter cold.
The Death Valley can be visited from November to March, the best time is February and March (it reduces the risk of cold at night). This period is generally recommended for the hot desert areas.
The Grand Canyon, to avoid the summer heat in the lower part as well as the cold of the upper part, can be visited in April and October. The high mountain areas of the Rockies, including the Yellowstone National Park, can be visited in the summer, from June to August.
New York can be visited in May and from mid-September to mid-October; the latter is generally a mild and relatively calm period. In winter, there's the risk of bitter cold and snow storms; in summer, of uncomfortable heat and thunderstorms; on early spring, of an unstable weather.
This period of early autumn is good even throughout the north and north-east, but also for the highlands of the western area, bearing in mind that at night it can be already cold. Even May is a good month for these areas.
Miami, the Everglades and Southern Florida can be visited from November to April, but for beach life, avoiding the risk of the rare but not impossible cold days, you can choose the period mid-March to late April.
March-April and October-November are good periods to visit the southern regions and those bordering the Gulf of Mexico. In the former, however, tornadoes are possible away from the coast, while in the latter, especially in October, hurricanes are still possible. In winter the weather is often pleasant, but we cannot exclude short cold waves.

What to pack

In winter: in the northern and mountainous areas, clothing for cold weather, thermal long underwear, down filled parka with insulated hood, gloves, warm boots, winter hat; T-shirts and light shirts for hot indoor environments.
In New York, down jacket, gloves, scarf, hat.
In the Seattle area and the north-west coast, warm clothes, coat, raincoat or umbrella.
In Los Angeles and Miami, clothes for spring and autumn, umbrella.
In the southern states and northern Florida, clothes for spring and autumn, but also warm clothes and a warm jacket for the short cold spells.

In summer: in the northernmost areas, light clothing, T-shirts for hot days, jacket and sweater for the evening and cool days, raincoat or umbrella.
On the west coast, down to San Francisco, clothes for spring and autumn: t-shirt, shirt, jacket, sweatshirt or sweater.
In New York, Chicago, Boston and Washington: light clothing, t-shirt, jacket and sweater for the evening and cool days, umbrella, sweatshirt and pashmina for airconditioned places.
In desert areas and all the southern belt: lightweight and loose fitting clothing, sun hat, sweatshirt and pashmina for airconditioned places, comfortable and breathable shoes; in Florida and the southern states, umbrella or light rain jacket; in the desert, light scarf for the dusty wind.
In the national parks on the mountains: hiking shoes, jacket and sweatshirt or sweater for the evening, sunscreen, sunglasses, hiking boots, umbrella or raincoat.

Other resources available for the climate of the United States and of the overseas possessions:

American Samoa (Oceania)
Hawaii (Oceania)
Puerto Rico (Caribbean)
United States Virgin Islands (Caribbean)