The most obvious 'sight' is the Castillo de Santa Barbara, a fortress which soars above the beach, with fantastic views from the top over the city and coast (there's a lift cut into the rock that takes you straight up).
Alicante prides itself on its culture and there are dozens of museums and galleries. At Museo de la Asegurada, the modern art museum, you can check out work by Spanish greats including Dali, Miro and Picasso.
Just walking around the old town is a fantastic way to take in the city's sights – the steep, narrow streets are lined with whitewashed houses, historic buildings and picturesque squares.
There are many interesting places in the area that can easily be visited on day trips from Alicante. The World Heritage Site of Elche, famed for its exotic palm forest, is 20km away, and the train takes just 30 minutes.
The pretty old town of Denia makes another worthwhile trip, particularly if you take the narrow-gauge railway, which hugs the cliffs and crosses beautiful countryside.
The island of Tabarca, just off the coast, is another popular day trip destination with its old fort, quiet fishing village, fresh seafood restaurants and coves lapped by turquoise water. Boats leave frequently from Alicante and Santa Pola.