I would encourage you to avoid November if you can, you won't get the typical island experience, thats the wettest month of the year. We get monsoon like rains for days on end some years and the water viz is considerably lessened by the runoff. You can expect 18+ days of rain in November. Our rainy season starts mid October and goes until January with late October , November and early December being the wettest by far. The best time to visit is February - September/early October, with May - September/early October being the absolute primo months for diving (water 84f and 120'+ viz).
If you want to be in town (cheapest accommodations are all in town), Alton's is good - if you use them I would recommend staying at The Lighthouse Hotel nearby (
www.utilalighthouse.com) .
Another option would be Coral View Beach Resort (
Coral View Beach Resort – Utila, Bay Islands, Honduras) and their dive operation, Coral View Divers. Both of these dive shops are on the opposite edge of town and the hotels I mentioned are decent and away from the late night boom boom music.
If you want to dive with Bay Islands College of Diving, I highly recommend staying at Manurii Boutique Hotel (
www.manurii.com)
If you want peace and privacy and want to stay in the most beautiful part of the island, I would dive with We-Dive Utila , a small very well run operation based on the Cays (
We-Dive Utila) and rent a beach house at Treasure Beach (
www.facebook.com/utilabeach). We-Dive Utila will take really good care of you, Anke the instructor/owner has been teaching on Utila for 15+ years, she's awesome.
All the best and have a great time, whatever you decide.