I've had it in Indonesia and I think I might still have a packet of it somewhere - it's a nice enough coffee, but I wouldn't go out of my way to get it again. A lot of Luwak is made with what are essentially battery farmed civets and is quite cruel.Has anyone here ever drunk this coffee?: https://en.wikipedia.org/wiki/Kopi_Luwak
It's also known as "civet coffee." It's...interesting albeit very expensive unless you live in Indonesia apparently.
If you want a couple of interesting Asian coffee experiences, you could try:
A vietnamese drip. These are made with a strong roast and condensed milk. The formulation dates back to the French colonial period and was a solution for making coffee where reliable refrigeration wasn't available. It's made with a little filter dohickey that sits on top of the cup.
https://www.lonelyplanet.com/vietnam/travel-tips-and-articles/a-guide-to-vietnamese-coffee/
Killiney Street - this is a chain of coffee shops based in the eponymous Killiney street in Singapore and has a few dozen franchisees around Asia. They make a nice Hainanese coffee formulation. It's quite sweet, so you want to be into sweetned coffee, but it's rather nice.
http://www.killiney-kopitiam.com/
For a couple of things that are neither tea or coffee from Indonesia, you could also try:
Wedang uwuh: https://thedailyroar.com/lifestyle/wedang-uwuh-a-red-temptation-herb-drink-from-yogyakarta/
Bandrek: https://en.wikipedia.org/wiki/Bandrek