Living in England, my wife and I have visited most of the Canary Islands, which are just a short-haul flight away and are ideal for winter sun.
If you're looking for lovely beaches, it has to be Fuerteventura. Some of the beaches are absolutely stunning! You need to rent a car to get to the best beaches (car hire is cheap, check out Pluscar). Fuerteventura is a long thin island, the best beaches are in the south. There are lots of hiking trails there too.
Lanzarote has fewer nice beaches, and is rather more touristy.
The beaches in Tenerife are awful! Black volcanic sand.
Gran Canaria is extremely busy and is perhaps best avoided.
I wouldn't say that any of the islands could be regarded as having particularly good food. There are some decent restaurants though, and TripAdvisor is the place to look.
Our favourite beaches are about 10 minutes' drive south of Costa Calma in Fuerteventura. Our all-time favourite is Sotavento (see pic) and just a bit further south is Mal Nombre. Sotavento is beautiful but there are no facilities. Mal Nombre has a beach restaurant, toilets, rental sunbeds, etc.
We're naturists, and most of the beaches in Fuerteventura are naturist, so you can wander for miles along the water's edge. If you don't want an all-over suntan, don't worry, naturists and textiles happily inter-mingle on the beaches.
One of the hotels we quite like in Fuerteventura is VIK Suite Hotel Risco del Gato. It's very quiet, has large individual suites, each with a jacuzzi and a totally private outdoor courtyard with sunbeds.
