I used to go to the Costa Blanca every March for that very reason. There is a great variety of cycling in the Benidorm area, including the 1,000 metre Tudons climb just behind it.
The hotels are still very cheap at that time of year and the CB has about the best climate in Europe for early spring sunshine. I thought about suggesting a CC cycling holiday there but the responsibility of organising it would be too much. Trying to get the cash out of people in advance and so on. The alternative would be to let people book their own rooms but then you couldn't get the discount prices, and would have to sort out your own airport transfers.
I think Tenerife might be a bit extreme for a forum holiday. I have a mate who has lived there off and on for about 6 years and he tells me that Teide is a monster climb by any standards, and that is the biggest cycling attraction there.
As for a weekend ... I would want to go for at least a week. 2 half-days are spent travelling but I suppose you could get rides in on those days if you timed the flights properly.