Although I’ve selected to show the Like button (and the Send button) under Like Button Settings for archives, pages, and posts, it only consistently shows up on posts. It shows up on some of my pages and not on others. For instance:
I upgraded to the newest version of the Facebook plugin today and still no change. I’m running WordPress 3.5.1.
The only correlation I can find is use of the Display Posts Shortcode on those pages where the Like button does not appear. That shortcode, however, is crucial to my display of database-based lists of information on certain pages.
Both referenced URLs appear to be pages: Cocoa Beach is page 2244; Orlando is page 2148.
Like button inclusion or exclusion happens by post type unless custom code on your site changes defaults. In this case both pages appear to be of the same post type and would therefore be evaluated the same.