Diving the Bay Islands is great....I will say, and this comes from an inveterate Utila lover, that the diving off Roatan is better. They seem to take better care of their coral...and the coral keeps the fish...also there are great coral canyons there.
La Ceiba gets ever rougher and more run down...I used to be an apologist for the place....but now I say, without reservation: There is nothing there that you want to see. the outlying areas still have great nature, but the town is scungy.
San Pedro Sula is a dangerous town. I´ve never had anything really bad happen to me there, but I get a bad vibe from the place, and you get a lot of stares on the streets when you are there, and folks ¨pace¨you, which means that they´re scoping for weakness...I would try not to spend too much time there either. If you´re that ass Robert Young Pelton, go to town.
Copan is very sleepy and nice....Just walk to the ruins...don´t let anybody convince you that you need to take a cab or something. This is because it´s a nice walk...and there are actually ruins that exist in situ along the path in people´s fields and things.
Three weeks is not a lot of time...so forget about Antigua, since it is just a more built up version of Copan....Go to Rio Dulce, which bypasses a lot of trouble, and from there head straight up to Flores and visit Tikal...Then it´s a straight cut across to Belize City, passing the Cayo, which is worth a look, if you have the time. Belize City is worth a quick beer-while walking-to search for a way to get away from Belize City. I assume you fly out of there, so the best place to go for a relaxing couple of days is probably Caye Caulker. Nice island. Bring repellent...Sand fleas.
Good luck...I´m tired of typing.
D