Splash Inn right in the heart of West End would be a safe choice. I've stayed there several times and it's a basic room for a reasonable price. $55 per night SINGLE... That includes A/C, WiFi and cable TV. Their dive rates are pretty good too, $25 per boat dive if you do at least 10 during your stay.
Roatan Hotel Dive Resort SPLASH INN West End Honduras
They have a dive shop on premise, but there has been a lot of changes recently, so I can't personally attest to how well the dive shop is running now.
If I were you, I would HIGHLY recommend diving with either West Bay Divers,
West Bay Divers | PADI 5 Star Dive Centre located on Roatan or a new shop named Seaquest Roatan
https://m.facebook.com/profile.php?id=263526347191527&_rdr . I believe West Bay Divers docks their boat directly in front of Splash Inn, so you could probably ride the dive boat to West Bay each day. Otherwise it's only $3.00 for a water taxi to West Bay. West Bay Divers specializes in small groups and if you check on Trip Advisor I believe they are rated #1 for West Bay.
I know the owners, instructors and divemasters for West Bay Divers and Seaquest Roatan and I'm sure you will love either dive shop. If you need further information feel free to PM me. If you want some other recommendations less expensive than Splash Inn, then just let me know. Just be aware, if you find something for much less than $55 per night, it will be much more "rustic" or not located directly in West End, which means inexpensive taxi rides. West End is very safe, but you don't want to venture too far off on foot away from West End. One of the cool things about staying in West End is that you have your choice of many, many restarants, bars and diveshops, all within a 10 minute walk up and down the street.