MDA diveshop in Guam also has an awesome program for FREE guided beach dives during the weekend. Of course you can pay to get on one of the boats to dive which start at $30 per dive. I opted for the free beach dives which are guided by newly certified divemasters looking to build up their experience. Carpooling is usually possible and you can rent your gear at the shop. I brought my own gear, so for me it was just a $5 for a tank with $3 refills! Current prices can be seen here. The other thing I liked about MDA is you get the gear/tank for 24 hours not per day or dive, so can you extend the diving over a couple days which is what I did. There is a big military presence on the island so the dive shop is usually busy and gets manic over the weekends. Some of the dives are on the military base so you would need to be a US citizen and have someone 'sponsor' you to get on base to dive these. There are plenty of dive sites not on the base, but the closest ones to the shop are so if everyone can get access they will go there. The visibility was very good with at least 15 meter visibility; 20 meter plus visibility is not unheard of, but the average is usually in the 10-20 meter range.
I heard great things about diving the Cocos islands which are off the southern tip of Guam. This is one of the further dives, but worth the effort from what everyone was saying. The dive boat was going there once every other week weather dependent, but could add more if enough people signed up.
I would recommend getting a rental car to explore the island, as the island is not exactly small and there is no public transportation. Cars Unlimited Ltd. was offering for $25 per day and I think even others were matching their price. Just confirm the booking in advance and have them pick you up from the airport as they do not have a desk there. All the car rental places at the airport were fairly pricey when I checked, but hopefully this has changed.
There are no hostels on Guam as of writing but there are some hotels in the $50 a night range; not exactly an ultra-budget destination. If you're a couchsurfer or can find cheap accommodation from someone willing to rent out a room to you (airbnb.com or wimdu.com) then I would rate Guam as great budget destination, especially for diving!