First of all there isn't any beaches within a 20 minute drive of Corvera, there is a very good selection of beaches around but they are all 45-50km from the resort
Going towards the airport at San Javier you have 3 choices, the first beaches around Los Alcazares, Lo Pagan, by the walkway to La Manga which are all of the Mar Menor with a good choice of restaurants along the fronts, loos but peak season parking can be tricky. The Mar Menor isn't the med, the water is warm and very shallow but there are still issues with water quality due to the flooding.
Turning left onto the N332 then the have the beaches on the med, around Torre De La Horadada, godd parking in large car parks, beach bars, loos and the ckeaner water and waves on the med
Abount the same mileage but more traffic on the smaller roads you have the beaches of Mazarron, wonderful beaches, restaurants around the harbour and boat trips. Parking can be difficult in the peak season but normally of you are willing to pay park in the harbour underground
Great site to see reviews on all local beaches, www.onthebeach.com
There are plenty of choices for restaurants around Thge Mar Menor, try Little Scilly and Lusines, reviews on Trip advisor, best steaks, Gaeigo in Pillar Venta Puerto is in Banos Y Mendingo, yes locals favourite