Gilli islands would definitely be a nice place to hang out for awhile during your DM training but the chances of finding work as a DM there are pretty much nonexistent because of what Limbo1 said.
The diving is fairly good - I just dived a few days there and saw turtles, sharks, cuttlefish, octopus and nudibranchs, but the coral is in terrible shape, at least what I saw on my few dives off Gilli Trawangan - don't expect to see colourful coral gardens like in some other parts of Indonesia, the Gilli reefs (at least Trawangan's) are pretty trashed sadly.
By the way, don't even consider a dive shop that won't offer you unlimited diving during your DM training! I think this is one of the most important things and should be a given.
Where ever you decide to go, before you decide on a particular dive shop, go in person to several dive shops and talk to the instructor that you would mostly be training with. Ask questions. Try to have a drink or coffee with them if possible outside of working hours to get to know them a bit. The dive master course is a lot of work and takes a long time. You will be spending lots of time with your instructor and it's crucial that you get a good feeling from this person. If the shops vary a bit in price (not sure if they do or if they will all offer the same exact rate) then don't just go with the cheapest one! Go with the dive shop and the instructor that you get the best feeling from.
There are so many factors that will affect your experience while training as a DM - do you want to go with a large, busy shop where you will get to assist with lots of courses where instructors are teaching relatively large groups? Or a small, relaxed place where you will be assisting instructors with small groups? Do you want a dive shop that is preparing you for a career as an instructor? Or are you more looking for an opportunity to do lots of diving and learning but not really interested in pursuing diving as a career after you finish your DM course? Do you want a dive shop that will have you doing lots of "grunt" work such as filling tanks for hours, hauling tanks, cleaning the dive shop and equipment, etc.? Do you want to be the only DMT that a particular instructor is training so that you get one-on-one attention or would you prefer to be with a dive shop where there are many DMTs? My point is people do a DM course for different reasons and their experiences vary widely depending on the dive shop and the instructor so CHOOSE CAREFULLY and make an informed decision.
Good luck and enjoy....
