I think a worthwhile tangent to ask...from the perspective of English-only speakers traveling to dive Raja Ampat (live-aboard I presume) or Komodo (live-aboard or land-based options), not just 'on the boat' but in terms of making one's way through airports, an over-night hotel if you get there a couple days early, etc...how 'easy' (or difficult) is our newbie American dive tourist likely to find it to communicate?
No plans soon, but one of those is on my hope-to-be-blessed-with bucket list. I've noticed the Philippines are closer, but I'd heard those 2 and Papua New Guinea were in the 'best coral reef diving in the world' category, and I hoped to hit one of the 3 before I kick off one of these days. So would be good to know. Thanks.
I'd say the eastern you go in Indonesia, the more difficult it gets.
There are "tourist area pockets" where almost everyone catering to tourism would (almost) understand you providing you avoid long sentences or fancy vocabulary. In Bali almost everyone on the main road speaks english, whereas this is less true if you take a scooter and drive in the inside of the island. Labuan Bajo or Sorong hoteliers will be able to meet you in almost proper english (although you'll be sometimes "surprized" with their way of dealing things... anticipate that something booked doesn't necessarily means it has been, unlike Phils or Thailand.) once you leave your hotel, it's better to have some bahasa (Indonesian language) words in mind like numbers (even though they will show you the price you should pay on a pocket calculator) . Airport is no problem, it can be more difficult with taxi drivers if you don't know precisely where you are going.
When I was traveling Maluku, east Flores or South Sulawesi for instance, I had to bring my bahasa phrasebook (or remember some bahasa words I have used during my 20 years experience in Indonesia) otherwise I would have barely known what to eat, nor found my way.
Clearly you'll need to have some bahasa language survival notions if you want to wander though local markets. But to be honest "survival" bahasa is easy and fun.
On the other hand, North Sulawesi people are quite fluent in english, maybe due to the dominant Christian religion/education.
Bear in mind that the lesser your interlocutor knows english language means the lesser he will be accustomed to tourists, the lesser risk of an intended scam. It's when the folk in front speaks your language that the odds are higher he's after your bucks.
As Chilly says above it's a tourist friendly country, just have some patience and anticipate.