I make the trip from Jakarta to either Indianapolis or Fort Myers at least once a year. Honestly, it does not matter which way you go, east or west. I pick flights based on price and connections. Right now there are two options with the best prices and times:
1. You can go "west" from the East Coast of the US. United/American/ANA/Japan Airlines will take you over the Arctic to Tokyo and then on to Jakarta. Just watch that your connection in Tokoyo does not require an airport change.
2. Qatar Air will take you east to Doha and on to Jakarta.
I actually prefer the Tokoyo route as the NYC/Japan fight is only 12ish hours as compared to 15ish from Doha to NYC. For me, anything over 13 hours is super brutal. There are also very simple "sleeping rooms" in the Tokoyo airport that are CHEAP. They are nothing more than a single bed and a small shower, but only cost like $30 USD for five hours. Also, if you look hard enough, you can find great prices on premium economy seats for the long flights. That extra money for the bigger seats is worth every penny.
Qatar Air and the Doha airport are really nice, but I have to disagree about the ONYX airport hotel being affordable. I think last Xmas, we paid a bit over $300 USD for six hours. Ouch. Food and booze in Doha are crazy expensive, too. Qatar Air does not do premium economy, but every now and then they drop amazing prices on their business class. If you find one of those deals, go for it.
Another option:
A friend booked premium economy seats for this summer on Singapore Air for the Singapore to JFK endurance fest: 18+ hours!!! ...and the same price point as the options above. No way would I do that, but for some, it might be worth exploring.
I hope this helps.