Be sure to check
http://www.ValenciaMan.com/alicante/alicante-hostels.html for "cheap"-er hostels/"hostales"/"pensiones". Only a small few have websites.
It's pretty darn difficult to find a private room for €20-30 per night in PEAK SEASON summer, however, so prepare yourself for that.
Casa Miguel has a private individual room for only 24 Euros per night with a shared bathroom so this might be your ONLY option.
Hostal-Pension La Milagrosa also has an individual room in this price range.
Best of luck and enjoy Alicante City! I like it a lot!
Saludos, MadridMan
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