We, my wife and I , had a smashing holiday in Alicante. Just a few days, but a it's a great city to visit.
We stayed in a B&B type hotel on Rambla Méndez Núñez. That was a more or less picked at random, but turned out to be a really good location. A stones throw from the old town and a short walk to the beach. The beach is incredible. It's right on the city doorstep. Good food. Reasonable prices...best I know of in Europe.