Utila is a big backpacking destination - surprisingly since it's a small island off the Honduran coast.
On the ferry over there were 3 groups - about 10 divers, about 20 backpackers and the rest locals. Rooms in town are really inexpensive and dives should be around $35 in any sort of package deal. In the spring it's also reliably possible to snorkel with Whalesharks there.
A cheap way over ts the
Utila Dream ferry from Roatan or La Ceiba on the mainland - either is about $30? but San Pedro Sula (the airport you fly into) is pretty unsafe so I would assume getting out of there backpacking is also - I think La Ceiba is about a 4 hr. drive from there.
Every summer they hold
SunJam on a nearby Cay - probably the only time it's
really crowded there. This year appears to be Aug 4th-5th.
There's also a couple hostels on Roatan -
Chillies in the West End even has their own dive operation - Native Sons. Food is reasonable in that area also. Dives cost the same if you wanted to split your trip between islands and the ferry picks up off the West End dock for Utila. There's a lot of $20 rooms in the West End also, double that buys you a kitchen. Out front daily a variety of fruit, produce and fish trucks sell fresh stuff - all properly iced etc. We bought from them more than once. Two small markets in town also.
You can also to fly out of Roatan or the mainland to Utila, the Utila airport is a day-use grass strip and the flights tend to be pricier. I think I've seen about $150 r/t from the mainland to Utila.
Worldwide Travel lists the local options - Alice lives there. Roatan from the US will be a pricier flight.
Either Utila or Roatan have probably in excess of 2 dozen dive operations - both turn out a lot of DM's. So you can easily get your advanced at either. I don't really know the in-town accommodations/dive operations since we stayed at a nearby AI resort.
Here's some links:
Utila Official Site - Utila, Bay Islands, Honduras - Tropical Island Paradise
http://utilaguide.com/
Roatan Bay Islands, Roatan Hotels, Resorts, Diving, Real Estate, Tours
Roatán - Honduras.com
Coconut Tree Divers also has a West End focused website - the Roatan section has some general info:
https://www.coconuttreedivers.com/