You could have a private small cabana at Tropical Paradise with a tv, a/c and fridge for close to your price. firstname.lastname@example.org is their email. They also have plainer non a/c rooms and cabanas for less. Restaurant on site. Nice dock to swim off.
The best accomodations are at Iguana Reef Inn. While they are priced higher than you wanted to pay you indeed get what you pay for. All rooms with a/c and stocked mini-fridge. No tv in rooms but in the lobby. Free coffee or tea in the lobby each morning. www.iguanareefinn.com
is their website. They also have links to lots of things on the island of interest. New bar on site perfect for watching the sunset with a cool one.
Generally Caye Caulker is less expensive than Ambergris so it does attract a mixed crowd. The young backpackers discovering Central America know that they can get very basic lodging on the caye without blowing their budget. It's fun to talk with them about their travels.
I'm a good bit older and appreciate and can afford nicer lodging. More and more people like me are going to Caulker. I like it because it is quieter and there are no busy streets with cars. You can walk everywhere in minutes. It also stretches my budget enough to allow me to have several trips per year. Diving is good and low priced. Since I spend most of my time underwater I am usually too pooped to look for nightlife. They have a disco if you want to do the night scene and there are a few bars that have occasional live music. I often travel solo and always find people to talk to and have fun with.
You can tranfer between the two islands via water taxi and then when it's time to leave to the airport fly right to international from either island.