I think Geocaching is a fantastic activity for families with kids. First and foremost, it gets kids (and parents) off their beehinds and out into the natural world while still being able to use the technology they all love. Even the best technology won't put your right on a cache so they have to look and think about where the cache might be hidden. Maybe interpret a clue from the cache owner or in the logs of other cachers. Most kids love the idea of a "treasure hunt" even if there really isn't any treasure. Pick up a few trinkets from the dollar store, junk drawer, or closet and can you show that it's sometimes better to give than receive. If you pick caches in parks or outside of town, there are so many opportunities see and explore the natural world around them. From wildlife to plants to streams and rivers to hills and valleys and more importantly a way to discuss those things and their importance with your children. Ask them why they think, for example, if there is a fence in the middle of the woods miles from the nearest home; who might have lived there before, what they did, and how they lived.
Secondly, it's a very inexpensive activity because most people already have smartphones and you really don't need much else. If you're going off the beaten track, maybe a pair of hiking boots but many of us have an old pair of shoes that could get muddy or wet. Maybe a Premium membership but that's really not necessarily, at least initially. It's also an opportunity for parents to show their kids that they can have fun without spending the price of admission at some theme park.
Thirdly, you can Geocache almost anywhere, it doesn't need to be a all day activity, nor does it really require any advanced planning because you'll have your phone and probably a pen in the car. One parent told me it was a great way to keep one kid occupied while waiting on the other to finish sports practice.
Have fun!