If you are looking for medium range prices, good selection, small little shops with locally made goods go to the West End.
If you are looking for high quality souvenirs at a bit higher of a price go to Mahogany Bay Cruise Ship Port which has a ton of nice shops. You would have to go on a cruise ship day. They carry mostly foreign brands. Anthony’s Key also has a great gift shop for t-shirts and flip flops.
If you are looking for cheaper souvenirs go to Coxen Hole, better to go with a guide on this one as prices will vary wildly. There is a really cool store in Coxen Hole called “Made in Roatan”. They specialize in locally made souvenirs and all the profits help local artists.
Also there will be people walking the streets on West Bay Beach and in The West End selling their goods. Stop and take a look, they have really nice things at good prices.
If you are looking to buy Jewellery, Diamonds International has great watches, necklaces and rings at amazing prices because it is duty free. They have about 150 stores world wide and are just as reputable as Zales or Peoples.
If you need to buy electronics in Roatan (cameras, electronics, chargers, memory cards, etc.) the best place is Technos Design in Coxen Hole.
If you are looking for a one stop shop for groceries go to Eldons or Plaza Mar in Coxen Hole, which is right near the airport.