There's always the Utila apartment finders, you can track him down on the internet, email or phone them up, tell them you're coming, have them meet you and start showing you apartments when you first get to the island. The only problem with this route, I hear, is not everybody wants to pay the apartment finders their finders fee so they don't have access to all the vacancies.
Or, you can stay at Cross Creek your first night and simply walk around and ask around. I found a place at the nursery, quiet, no vermin, nice deck, good location in about two hours using the walking and asking method. Everybody knows somebody with a place for rent and won't hesitate to call the landlords for you as a favour to their property owning friends. I found the nursery place through Lazy Daze on the Bay.
In 2011 I stayed at Maggie's place. highly recommended. I paid $450/month + electricity for an almost new concrete apartment with double pane windows ( great for noise as it's right on main Street ) no bugs or vermin, big covered patio with BBQ, secure location, internet, good kitchen and it was proper clean, not Utila clean.