Tenerife certainly fits the bill. This beach was about 200 m from the conference room. I was able to go swimming most days after the presentations ended, I also did some climbing on the rocks in the left of this picture and jumped off them into the water, which was cold but very refreshing.
It was a serious conference, but with a very upbeat and fun vibe. On Tuesday evening they had a session for impromptu talks on work in progress with the traditional unlimited rum from the conference's Caribbean origins. I mistakenly gave a serious talk about online protest, with a mixed reaction, though I did work a few off-color jokes in.
The island itself is surprisingly large and has very interesting geography due to its volcanic origins. This peak here is El Teide-at 3,715 m it's actually (by a good margin) the tallest peak in "Spain," though geographically quite far from the mainland.
The island also has a fascinating history. The Spaniards have been there for quite some time and built some very nice villages in the hills, like this one, La Laguna.
Walking around there are dozens of open-courtyard homes like this one with beautiful gardens built by the old nobility. It's enough to have earned UNESCO world heritage status for the town, which they are happy to remind you of as they try to sell some of the local fare-a fortified wine called Presos Canarias and rum-laden honey.
Much of the island feels pretty touristy, which it is, as a major destination for Germans and Brits. I didn't feel like I got a very good impression of the local scene, but I did get the biggest pizza I've ever seen served to me, which I was unable to finish.
Still, was a nice break from the Cambridge winter and for the £40 plane fares you can get I'd consider going back.