akennell - Welcome to the forum, and please forgive folks that like to play games instead of providing what they know would be helpful/useful information (or just keeping quiet).
The island is flat, so in typical terms of hiking, there isn't any on the island. The island is appx 28 miles long, so there's plenty of walking available, but no real elevation. Biking is the most popular form of getting around to see the best of Ambergris.
On the mainland, there is plenty of elevation in the San Ignacio and Maya Mountains areas. You'll want a guide, as there are also snakes and plenty of heavy jungle as well. Ian Anderson's Caves Branch would be the first place that would come to mind to ask about any kind of scheduled/guided hiking activities. If they don't offer that service, they would most likely know others that might. I know that Chaa Creek and duPlooy's Jungle Lodge (my favourite place on the mainland) offer wonderful guided tours of their grounds (mainly flora and fauna tours), but might also have some more adventurous options as well.
Here are links to those locations, and perhaps others with actual helpful information/experience will chime in as well. Victoria House is amazing, and I'm sure you'll have an amazing time!!http://www.cavesbranch.com/http://www.chaacreek.com/http://www.duplooys.com/
All the best!