Benidorm weather is not unpleasant at any point of time during the year. The summers however can get pretty hot so be careful. The weather is largely good all year around but depending upon where you are coming from you might find one of the two seasons more favourable. Take your pick.
Summer: You need to remember that Benidorm can get quite dry in summer so you need to carry around a lot of water. The temperature may reach up to 35 degree Celsius but not more than that so weather can turn out to be great. June to September are great months to visit. Most water parks are only open during summer.
Winter: In November it rains a bit but other than that the weather is very mild. You may not get the sun as you expected from the Sunny Spain but there is a lot to do despite this.