Most piers are public, although if its posted private, please be considerate of the owner's wishes. The beaches are public, but in my opinion, the best swimming is at the "Split" at the north end of the island, where there is a channel dividing it in 2. Its about a 15 minute walk (north) from the Water Taxi pier.
There are no ATMs on Caye Caulker, but there is an Atlantic Bank that you can get a cash advance from your Visa card. Most of the larger hotels and restaurants accept credit cards, although American Express is not widely accepted, Visa and Mastercard is, with preference given to Visa Cards.
When you say "budget" for accommodations... what is your buget per night?
[This message has been edited by Cybercayecaulker.com (edited 03-21-2004).]