Try a "search" here on SCUBABoard for answers to a lot of your questions.
Usualy, if you want to stay at an AI on Roatan, you would arrange the air through them or with their stateside booking agents. You're going to need a ride from the airport. No big deal, but an AI would make that an inclusive done deal.
"Major" AI resorts? Look at AKR (Anthony's Key), IoLR (Inn of the Last resort), BIBR (Bay Islands Beach Resort) along the NorthWest side. On the Southern shore, look at FIBR (Fantasy Island) and CCV (CoCoView). These are the major players, others will chime in and tell you about how their experience at this or that or yet another resort was just the best ever. Everyone has an opinion, some are more broad based in terms of experience than others.
You have to know what you want out of a vacation and state it as such.
You want a high end resort, but then you talk about getting meals off the homestead. It's entirely possible and can be fun for some, but you kind of have to decide what you want: A dive vactaion... or a vacation with diving. If you want a dive vacation, this to me means 3 to 4 each day plus a night dive. If you don't mind missing 2 out of that daily schedule, eating out for dinner is an option.
All of the AI's are safe, as a matter of fact, the island is safe. If a tourist gets into puppy-poop on Roatan, they had to have been looking for it. Universal truth: The farther you distance yourself from locals who are out drinking, the better. I have still had nary a problem at any local joint... never! But then again, I do not drink, I smile a lot, and I don't flirt with their sisters or girlfriends. The same rule would apply in Peoria.
If you are talking about "safe" in terms of isolation, CCV would be the one as it is on its own private ten acre island. No one there but staff and guests- all other resorts have frequent traffic from locals. At CCV, you may be able to leave cameras lying about and your rooms unlocked... downside? Your'e not within walking distance of several fun and happy West End bars. But at CCV, you are there for the diving.
For your possible wide ranging desires- don't forget to look at the non-AI options. There are numerous cottages for rent in the West Bay area, great day-dive ops, as well as tiny AI's located in Oak Ridge. Again- use that "search" capability on SCUBABoard !
Never, ever rent a car. The liability issues are extreme, the roads suck- and you won't know where to go or park. There is simply no medical assistance above band aids. Hire and English speaking cab driver for the day. Select from a run-of-the-mill island tour to a real east end adventure.
A day trip to Belize? B.Y.O.H. (Bring your own helicopter) It aint happenin'. You are going to see the same reefs, structure and critters in the Bay Islands that you'll see in Belize... a mere 90 miles away. There are flights during the weekdays, but it is not a real option for divers. You could hire a boat if you have the $$$. Better to take two weeks and do both, 1 week in each.
Roatan can be enjoyable for diving vacationers of many sorts, it is not yet Cozumel (thank the heavens), It's a long way away from it's Cayman cousins, and for many- the diving is disappointing. Many divers arrive only understanding how to see lobsters, crabs or fish that are bigger than a college textbook.
Roatan is for the diver with good to perfect buoyancy skills, someone who doesn't view a dive as a race, someone who brings a flashlight on each and every dive... and someone who is interested in what you're looking at with that magnifying glass. Looking beyond the hype promulgated by some resorts, interest groups and salesman- finding the kind of experience you want- that's the key. There is precious little to do (yet) on Roatan other than dive- don't really think otherwise... yet.
Something for everyone- but nothing for the diver who comes looking for what they have already seen in the rest of the Caribbean. Find a good DM and stick your faceplate on his flippers. People post all the time asking if the DM's hover over you. No- they are the least invasive in the Bay Islands than any Caribbean destination, but as they see more dunderheads (now that the island is being "dicovered"), that will likely change. If you toddle off on your own, you are likely to see nothing. It took me 100 plus dives in the Bay Islands before I knew where and how to look.
Rely on a good DM.