I can't comment about security coz I'm biased (I'm Indonesian), so I'll try to give pointers about the diving instead. Sulawesi is fabulous, try to make time for other sites besides Bunaken:
- Likupang
- Bangka
- Lembeh (a must!! it's simply fabulous!)
I'd highly recommend
Eco Divers operating out of Tasik Ria Resort - fab boat and guides, and great accommodation.
BALI
I go home to Bali to dive 3-4 times a year, and I'd strongly recommend that you go with a reputable dive operator. There are about 150 dive operators in Bali, and only a handful of good, responsible, safety-conscious ones. Don't be tempted by rock-bottom prices - this can only mean they cut corners and therefore put your safety at risk.
Most of the dive ops can pick you up from your hotel at no extra charge, and drive you back after the dives. They will even wash your gear for you

Jimbaran is not "in the middle of nowhere", just a wee bit off the main road
Here are some that I would recommend (I
don't work for any of them, I'm just a very satisfied customer

)
-
Bali Scuba
-
Waterworx
As for sites, depending on what you want to see, here are some recommendations:
- Nusa Penida: pelagics, walls, clear water, drift dives. (Top site)
- Tulamben: wreck, macro, lots of fish, wall. (Best, easiest wreck dive in Asia IMHO)
- Menjangan: Wall, pelagics, clear water (depending on season)
- Secret Bay: macro
- Seraya: macro
- Puri Jati: new site... I haven't been yet but I heard there's a resident colony of mimic octopus
- Padang Bai: reef, wobbegong sharks, macro.
- Gili Selang, Biaha, Tepekong: drift, sharks, lobsters.
If you want to find out more about Bali diving, from people who actually live there, check out this
local diving club's website.
I hope this helps.