Alright...let me try to help a bit. These are just generalizations and there are many exceptions to the following, but this should help you get the lay of the land for a first trip to Indonesia.
For the most part diving off Bali is off the east coast and centered in three general areas: Tulamben, Padang Bai, and Nusa Penida/Nusa Lembongan. Any diving advertised in Sanur, Kuta, Legian, Seminyak, Nusa Dua, etc... are really just shops that will stick you on a bus and/or speed boat and take you to one of these three areas.
With a few exceptions here and there, mainland Bali diving is muck diving...fantastic muck diving...but really about photogs getting the opportunity to shoot amazing, tiny creatures. I love muck diving more than anything, but it isnt for everyone and often not what many people think about when coming to dive this part of the word.
Two islands (named Nusa Penida and Nusa Lembongan) about 30 minutes off east Bali make up most of the coral and pelagic diving. Here you can find seasonal mola mola, mantas, turtles, some sharks, etc... along with solid, healthy coral. Be aware most of the diving is in manageable but often quite fast current. You can stay on Nusa Lembongan in a number of resorts that range from backpacker to posh. I usually dive with Two Fish. To get there you will go 35-45 minutes from the airport to the harbor at Sanur then fast boat across maybe another 30-40 minutes.
Padang Bai is a small fishing town that has embraced diving and a ferry boats to Lombok economy. In many ways it is the best of both worlds as the muck diving nearby is awesome. It is also an acceptable run by speedboat to dive the islands, including Nusa Penida, off shore for big pelagics. It is about 1.5 hours from the airport. I am a huge fan of Gekko Divers in Padang Bai.
Tulamben is a blip on the costal road consisting of about 25ish dive resorts and is 3+ hours from the airport. Again, the muck diving is spectacular. There are some decent coral sites too. It is most famous for a big wreck the USS Liberty that was wrecked onshore top save the cargo and later pushed back in the water by an earthquake. Take some time to read up on Tulamben and diving the Liberty as the crowds can be a nightmare. That being said, I very much enjoy diving Tulamben. I highly recommend Liberty Dive Center.
There is some solid diving way north around Menjangan Island, but I have never been.
Anyway, I hope this helps and started with your research to figure out what works best for you.
