Geocaching offers a wide array of ways to engage with the game most of which involve you signing your name as proof of a visit. Two notable exemptions to that are Virtuals and Earthcaches the former can only be published with a special award from Groundspeak and the latter requires attention to detail and a worthy geological location. Although there are hoops you have to jump through to get it published Earthcaches are the only permanent cache type available to anyone that does not require a physical log/container to maintain.
Part of the appeal above their uncommon nature is that generally speaking these are found at cool locations. When I travel I will often begin by looking at what high favorited Virtual and Earthcaches are in the area. This is often a better barometer for where you should invest your time then tourist websites. Cachers are by nature outdoorsy and addicted to the numbers (find counts, fizzy loops, etc.) but these caches are almost certainly worth the extra effort.
I was awarded a virtual cache when they were first brought back in 2017 and after some hemming and hawing I ultimately placed it in the Country Club Plaza a notable location in my hometown. A year later I decided to take the leap and placed my first Earthcache at Crown Center. As an indoor Earthcache focused on a waterfall in a beautiful spot that, I feel, makes it unique. Soon after that I put out an Earthcache near the oldest cache in the state and gave it an appropriately similar name of Watts Mill. As I love local history all 3 caches focus heavily on the background and story of their applicable area.
Over the years I've visited a lot of Earthcaches trying to get one in each new state I visit. To date I have claimed 172 Earthcaches in 26 different states. Here are a few of my favorite images.