Your question has numerous answers, America is so diverse in it's character you might have to visit a dozen places to see different interests. Here is a list relevant to a particular interest.
Arts Culture, Plays & Theater - New York City & Chicago
Scenic Ocean views, fishing & New Englanders - Boston to Maine
Tropical Ocean beaches - Hawaii, Virginia to Florida & Key West via the coast line.
Scenic Mountain Driving - Pennsylvania to South Carolina along the Appalachian Trail
Western Singers & Music - Austin Texas
Gambling Night life - Las Vegas or Reno Nevada
Loads of National Parks with camping, fishing, etc - Mostly western states.
California has a lot of everything including traffic jams.
The climates in all areas of the US vary a lot by the season, so if you like a temperate climate then check an area for seasonal weather conditions.
So enjoy, there is so much here to enjoy it is hard to summarize.