Anonymous wrote:"The idea of spending a week in one place hiking makes me feel kind of stir crazy and not even there yet."
So listen to yourself. Do what you want.
Do you like biking? Boats? Do you like small towns? Plenty of places with great outdoorsy activities are not all that far from nice towns and even cities.
Are you worried about your kids not being exposed to a variety of things?
Part of it I think is I didn't get exposed to these things growing up. We sometimes went to the beach and anywhere else we went was sightseeing history stuff mostly within our state. We never went on a hike or boat even around home. And never an amusement park--I went with groups, but not my family.
I like boats but some of the family don't. Biking is okay. Small towns are nice. Mainly I think an outdoor trip seems way harder to plan and more can go wrong like if we spend a bunch of money and it rains the whole time. Maybe you are onto something with starting with one or two outdoorsy activities that are close to a city or town and they can be moved around depending on weather.