Here's a link to a site with a list of banks in Belize:http://belizeretirement.org/banking.shtml
I chose the one that was best for me.
I don't know how many branches each bank has, but Belize Bank, ScotiaBank (no longer known as Bank of Nova Scotia) and Atlantic Bank seem to have branches in most towns and on the cayes. And ScotiaBank has branches in Chetumal & some other Caribbean countries.
ScotiaBank has a website: