Capri things to do

First off, get there as early as you can. There are plenty of day trippers that don’t arrive until noon or after, you do not want to be among them. The “laser” boat tours around the island are actually nice and a pretty decent deal. It’s only like an hour if you skip the Blue Grotto. Otherwise, when you get ashore skip past the tourist trap Capri Town and head straight up to Anacapri. It doesn’t get crowded until later and can be lovely. The chairlift up to Monte Solaro and it’s jaw-dropping views ranks among my favorite travel memories.

Lots to do on the island! Explore your options, based on your personal interests, here:

https://www.capri.net

You do not need any sort of tour to do your looking about, even though the website touts many of those. You are traveling with two young men ages 17 and 20, correct? I'd think they'd like to be as active as possible so trekking around on foot would be my vote + some other stuff. Our personal favorites:

The hike (actually more of a walk through winding narrow "streets") up to Villa Jovis:
https://www.capri.com/en/e/the-villas-of-tiberius

And Natural Arch/Pizzolungo coastal path
https://www.capri.com/en/e/pizzolungo-2

The chairlift to the top of Mt. Solaro (Anacapri). If feeling ambitious, walk down the mountain back to Anacapri
https://www.capri.com/en/e/monte-solaro-high-drama

Poke your noses into the Chiesa San Michele in Anacapri to admire the hand painted ceramic tile floor, and there is (I thought) a particularly lovely little cemetery just up the street from the chairlift station.

https://www.chiesa-san-michele.com/lg/en/index.htm
https://www.sorrentoreview.com/chiesa-di-san-michele-arcangelo-anacapri.html

\Map of Capri:
https://www.capri.com/en/map