The boats - mostly high-speed, which is what you'd want to take anyway - run from Sorrento and Naples to Capri all year. They HAVE to as residents on the island need access to the mainland. They just don't have as many runs as during high season. It's service to/from other points along the Amalfi (Positano, Amalfi, etc.) that stops roughly from November - March or mid-May.
https://www.sorrentoinsider.com/en/ferry-schedule
Service can be cancelled if the weather is bad enough to make a crossing hazardous, and they don't run after dark but if you're staying in Sorrento for a few days, you shouldn't have a problem making a trip to the island on a nice day. Besides, Capri wouldn't be any fun on a foul-weather day!
The best part of the island, IMHO, is just walking/hiking about and taking in the scenery so if you're good with exploring on foot, then I think you'll have a very pleasant day. The trek to Villa Jovis is highly recommended....
https://www.capri.net/en/s/villa-jovis-mount-tiberio
....as is the Pizzolungo walk:
https://www.capri.net/en/s/arco-naturale-and-pizzolungo
Take the little bus up to Anacapri and the chairlift to the top of Mt Solaro:
https://www.capri.net/en/s/mount-solaro-cetrella
Anyway, lots of fun walking (some of it can be a bit strenuous) and gazing to be had on Capri! Ignore the tours touted on the website: you don't need them. Just do a little reading before the trip, pick up a map at the tourist info center when you get there, and off you go!
Editing to add: Capri.net and Capri.com are essentially duplicate websites.
