We stayed a few nights in Alicante in October. Stayed at the Tryp Gran Sol, wouldn't call it cheap though, and certainly not the best hotel hotel we've stayed in. Went there for the view, so we couldn't complain from our 17th floor! Taxi into Alicante cost about 20 euros (late evening) but was much cheaper going back. We really liked Alicante, very Spanish, lots of places to eat and drink, nice beach, good shops and the castle is lovely. They are really developing the harbour area and some very nice hotels there. If you were lucky enough to get a special deal at the Melia, I'd take it!
kate

You wont find a hotel near to the airport, near to the "things to do",as Kate says it will be a taxi ride into the city.
The nearest decent hotel to the airport is the Holiday Inn but that is stilla bus ride into town.
I have stayed at The Melia,The Spa Porta Maris and the Kris Maya,all good hotels with the first two right on the front and a bit pricey.The Kris Maya is a 5/10 minute walk into the centre but a cheaper option but still good quality.

I am still looking but thanks for the info

I have booked the tryp gran sol for £60 for 2 nights ..it was a special offer, its usuually £120 so I grabbed a bargain