Seaside Cabanas had phones when I was there last fall. Only for the island, though. Don't know if incoming international calls can be put thru to room.
If you need to be reached, almost all places will deliver messages to you.
Don't know what you mean by inexpensive. Seaside quoted me a price of $50/night for one of the AC rooms. Nice amenities- bedside lamp, dining table w/2 chairs, small fridge, I think microwave? not sure ask them. Nice decor & what seemed like decent beds. Can be a bit noisy as it's next door to main dock/entry into town.
I've heard about the Disco Hotel. New rooms, hot bath, $12-15/night. Don't know anything else. Maybe someone here does.