Tenerife is much more than beach.
Actually, the beaches on Tenerife, while perfectly fine, pale in comparison to anything Florida or the Caribbean can offer.
Despite large numbers of visitors, Tenerife is an amazing all-around nature destination. Huge volcano in the middle, misty forests in the northeast (current status TBC after wildfires, though), rugged north coast, historic towns with 15-16h c. architecture (La Laguna, Garachico) that were later replicated in the New World ... It really exceeded my expectations when I spent a week there in October 2018.
However, art is not a focus, and the food is not as good as on the mainland in my opinion.
There are many other worthwhile islands in the archipelago (la Gomera is very easy from Tenerife), but I have no firsthand knowledge there.