Grand Cayman has some good shore diving, but I would not consider it a budget destination. One of the most reasonable hotels, the Sunset House, generally runs over $100 a night even in off season. Because of the currency conversion, everything in Cayman is generally higher than most other Caribbean locations.
Aruba is also generally one of the more expensive islands for hotels, but there are bargains to be found as long as you do not insist on going high season (Jan through April 15) and staying directly on Palm Beach. And while it doesn't have the vast number of outstanding shore dives that Bonaire does, there are several good ones and some cool wreck diving to be had there. Also, for activities above water, it is probably as good as it gets in the Caribbean. As I am always traveling on a budget, and like going to Aruba, I have sampled a number of the budget hotels there.
This December some friends and I stayed at the MVC Eagle Beach which is a converted Dutch Marine vacation club. Other than small plain rooms with small beds, it was clean and convenient and with good A/C, cable TV, a mini frig in the room, just across the road from a very nice section of Eagle Beach. It also has a very good and reasonbly priced restaurant onsite. Including the daily breakfast buffet, it was $60 a night per room. I would highly recommend this hotel.
Also the Mill Resort across the road from Palm Beach is decent and offers off season specials in the $80 a night range. Many of these units have full kitchens.
There is also the Aruba Blue Village. This is inland a ways and is somewhat difficult to find and the rooms are not in particularly good shape, but it is popular with the young Dutch women who seem to fill the place up in Winter. It runs from $75 a night up depending on room type.
The Coconut Inn is also a clean little hotel off the beach in the Noord area. They have a full breakfast and kitchenettes for around $65 a night and up.