Depending on where you go in the USA, it can be from the last weekend of May to the first full week of September would be considered the peak tourism season. The Northern states tend to have their school year run from the beginning of September to the 3rd week of June, in the Southern states, generally from early to mid-August to the end of May.
Perhaps the best months to be in the USA are May and September. September is best if in the Western states as little problems as to snow at higher elevations and moderate temperatures. May in the Eastern, Midwest and Southern States is better as after tornado season and before Hurricane season. SFO
tends to be quite moderate year round as to temps, but inland areas can be hot in the summer.
If you do choose to travel in June/July, try to fly mid-week and get in early in the afternoon before thunderstorms, which normally tend to be the worst for flying in the mid to late afternoon. If you plan to fly within the USA, also try to use off peak midweek flights to have the best chance of seats.