Try La Marina Village 30 mins from Alicante. We like the El Pinet end it is in a quiet rural area just outside the village of La Marina which is typically Spanish and you will be able to find a wide selection of pleasant bars and restaurants to suit all tastes. There is an English Butchers in the village, papershop, chemist, grocery store etc and a short 5 minute drive you will find a large supermarket and the new Iceland store selling all your well known brands.
The beach at El pinet has long been a favourite with the Spanish due to its beautiful golden sand and beachside eateries. Worth a visit on the beach is MARUJA HOSTEL El Pinet La Marina, elx Elche, Alicante it is found Amongst the more than fifty well-kept chalets that line the beach Hostal Maruja which has sat at the centre of this parade for sixty years and as you can see from the images, hasn’t changed at all. I have copied some of this off of their web page it is on the spain-info site. But it is possible to rent apartments in that area that are within walking distance of shops and bars.