If you are looking for a nice beach outside the city, not so crowded, Porto Conte is a good option. You can reach it by public bus. Ask at the tourist info. The buses leave from the park in front of tourist info.
It is not a marvellous beach, and the waters are too calm , as it is inside a bay, but it's not too crowded. There are a few hotels there in case you wanna have lunch or a drink.
We find by chance a very nice diving club on beach of Alghero, "via Lido 4" (15 minutes from the centertown). For a very good price we had a very personal service : only the 3 of us in the boat, you choose your diving sites (it was a great pleasure to dive in the Porto Conte Natural Parc : the wonderfull Nereo cave, other smaller caves and a lot of baracudas and octopus), we made a nigh-diving. The instructor is very friendly and the equipement is new and of good quality! Very good surprise, that why I took the time to make this recommendations, it is a great place!
His website (unfortunatly in italian...) : www.holidaysdivingcenter.it
Equipment: They provide all the equipement.
Excursions on the Porto Conte Natural Parc. Immersions on falesias and caves to see several mediterranean fishes species or marine vegetation. Nocturnal immersions are also possible. The organization provides equipments and excursions on request.
All levels diving courses with Divemasters and aid instructors; licences of Didactics NASE, CMAS and PADI