"Live free or die." It's about a good a motto as a state can have. (Missouri's "Show-Me" moniker isn't bad either.)
For me, New Hampshire is most closely tied to some very good family friends, who have close ties to New Hampshire. Some of them now live full-time in New Hampshire. During my time in Boston, visits to the coastal town of North Hampton, where they lived, were a regular highlight. They sometimes included walks to the water, or lobster boils, or fires. They always included slippers, delicious home-cooked meals, and cozy movie/ TV watching.
New Hampshire has very low alcohol taxes and very large state-run booze outlets, meaning that it was not a successful trip from Boston if the trunk returned empty.