All states in the United States will contain bugs but some places may contain a lesser amount of bugs which can make spending time outdoors much more pleasant.
However there are two places on earth that do not contain any bugs but they don't contain bugs because the bugs could not thrive there.
The two places on earth that do not contain any amount of bugs is both Antarctica and Iceland.
Those places are really cold year round and are no places for bugs or even humans to live.
The states that contain the least amount of bugs are Illinois, Delaware, North Dakota, Idaho, New Hampshire, Connecticut and Washing DC.
Other than Antarctica and Iceland there's no way to escape all bugs.