Many NTs wouldn't dream of going somewhere to be alone for a few days, even if they really wanted to, because of what other people might think of them. So if you do it, and don't act embarassed about it, a lot of NTs will interpret that as incredibly self-assured. Many will envy your freedom to do what you like without worrying about how it looks to other people.
Also, you might want to use the phrase "chill out" in your answer, as in "I'm going to the state park to chill out for a few days". It somehow lends an air of NTish respectability to choosing to be alone for a while.
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Ever tried. Ever failed. No matter. Try again. Fail again. Fail better.
-- Samuel Beckett