I don't recommend going ashore in Belize unless you have an excursion planned. You have to get on a boat and be tendered to the dock. It is a very poor area. Police wear automatic weapons and warn you if you leave the "tourist area".
A friend did leave to go to a local store and told us he was solicited for all sorts of things. He said a women cried that if he didn't give her money, her children wouldn't eat. People watched and followed him. They also charged him $20 USD for some rice which he didn't stay to eat because he wanted to get back to the safe area.
There was a small shopping area with the normal T-shirts, tourist items and jewelry. It was nice to walk around and had clean restrooms. We took a shore excursion and after leaving this shopping area, the area outside of the port looks very poor and road quality is questionable. Nice beaches and water. I think a planned excursion is the best way to see Roatan.
You have to be tendered to the dock. Lots of shopping and restaurants by the dock area, but they were chain restaurants. Walking a bit further into the city and we came upon folding tables and tents set up which were selling island food like plantains and curry goat.