At the hostel, we often have guests working while they're here, generally preferring to make the hostel their 'home' for several weeks or a month or 2 at a time, to establish a work routine and still have some free time to enjoy island life, and then they move on to the next location. I've had guests who manage Facebook and social media accounts, others who do IT work, do editing, do web design and graphic design, teach English, work as a travel agent- it seems like there's a wide variety of job opportunities to do remotely as a digital nomad. As an outside observer, it seems to work best when remote workers plan a set work schedule if possible, so that there are designated hours/days off to explore and have fun- occasionally I've had someone that seems to be busy working all the time, without taking the time to make the most of island life.
Doing this type of work means you need a fairly reliable internet connection, something that's not always a given, depending on the area you're traveling. On Roatan, for an island, our internet's pretty decent- though it's not speedy, it doesn't fail very often, though power outages can happen once a week or so. It's a good option to buy a local SIM card for your phone with the option to purchase a data package when needed, so that there's a back up connection if you have time sensitive work.
At the hostel, we have weekly and monthly rates, and have small, budget-friendly single options for solo travelers, so if you're working while away and need a little space to yourself, you can have it, including a few with desks. There's a communal kitchen, or also apartment style options that have their own kitchens. We have many guests that stay for a long time, so you'll have a great community to be a part of while you're here.