Hi Alison, Roatan is an island in the Bay Islands of Honduras. Unfortunately, travel to and from Belize to Roatan is a pain. When you say you want to travel around, do you mean travel around Belize? Lots of wonderful things to do there, but even though it is a small country lots of the great things to see and do aren't necessarily next door to each other.
For learning to dive, my recommendation would be to go to Roatan. Lots more young people there and if you hook up at certain dive ops, a social life comes with it. For example, Coconut Tree Divers. Myself, I dive with Westend Divers and have great regard for that op and love the manager Mel (Melanie) and her staff but not sure that there is a ton of mingling with the tourists. Whereas, Coconuts kind of fosters the social aspect. As a diver in training, being on your own will be no problem no matter which dive op you pick.
As for Belize, the majority of my experience, is on Ambergris Caye. I've not had any training in Belize but for a good fun shop, I'll direct you to Chuck and Robbie's. I love Robbie and have known him since he was a baby dive master.
For accommodation recommendations, I'll need to have a better idea of your approx budget per night. For starters though, look into Ruby's for very inexpensive but on the beach. But even better will be Tio Pill's, especially if you get a beachfront room.
For inland, go to San Ignacio. You must do the ATM cave day trip while you are there.
I'm not 31anymore but have been traveling worldwide on my own for years. You are right not to wait for friends to have the time and/or money to join you. I've been fortunate to make friends alongvthe way and have met my three best friends, while on dive holidays in Belize. I didn't meet them all on the same trip and they don't know one another. But having met them that way, I rarely go on trips by myself anymore because we are all kindred spirits!
Feel free to ask me anything. I'll give you the best answers I'm able.