I went thirty years ago with 6 year old DD, and found it absolutely beautiful, one of the most stunning places I've ever been.
Blue grotto - interesting and pretty but missable.
What I liked was wandering round Anacapri and the Villa St Michele (might have spelt that wrong) the little square, the shops, and the VIEWS. This tiny high lump of rock soaring out of the sea, and the glorious view looking down of a sparkling deep blue ocean.
Had a good meal at a hotel (pizza, probably), bought some fancy kids' clothes at an expensive clothing shop (because I did daft things like that in those days) and vowed to come back with husband and higher budget. I never did, and regret it.
I liked it better than Pompeii, although as a history/Roman enthusiast that was the main point of the trip, and I'm glad to have seen it (twice) but it was dreadfully HOT and rather crowded. However, it must be seen. That sinister but oh-so-innocent volcano looming at the end of the cart-wide streets....