Thanks to SouthWest, flight to Belize are really reasonable out of Houston. A trip to Ambergris Cay or Cay Cauker would fit the bill for fishing and diving. Small bonefish but legitimate shots at permit everyday you want to chase them. Plenty of residential tarpon.
For the tarpon at the flats you need small white flies, like sz 2 white toads or small decievers and even some surf candy style flies.