You could take a direct flight from Jakarta to Sorong, then on the way back go Sorong to Makassar to Bali, spend a couple of days in Bali, then fly to Labuan Bajo. You have to fly from Bali to get to Labuan Bajo..
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Bali has mantas all year round. You can head to Manta Point from Sanur or Padang Bai or dive from a resort in Nusa Lembongan. Dive sites are not usually crowded around mid to end January and May/June as the high season is August to November.
Bali is the easiest to get to but that needn't be your main motivation. The diving there is great, not just for mantas. You can also find much more affordable prices.
Raja Ampat can be a hassle to get through. January is better.
May/June is also good for Komodo.
In may the conditions in raja Ampat are windy in the south. Resorts in the north are still open.
Do consider that getting to raja Ampat takes really long time
Having been in Bali and raja Ampat if I had to go in January I would go to ra however tickets will be expensive at short notice
In may I would go to Bali
The mantas in Bali are more reliable than raja am told, although I just came back and we had many many mantas
Raja Ampat is remote and has got some unique features however Bali for me on land based is difficult to beat
So make your choice depending on the time you can go
3 to 4 weeks toucan actually combine Bali and raja or North Sulawesi