Currently in China and a new member on the forums but a long time drone pilot. I've flown in the likes of many SE Asian countries--Thailand, Sri Lanka, China-, Indonesia--and my best recommendation is to know the drone laws of each country you are going inside and out and absolutely be respectful of those laws. I definitely echo Thunderdrones list of points. I want to expand on a few points:
1. Again, make sure you're familiar with local laws and bring both english and host country translation of them. Most of these countries have a civil authority where you can find the local regs in the local language--generally speaking: line of sight flight, flight ceilings, no night time flying, etc. Thailand actually has relatively strict drone regulations, especially near military bases and they are not always captured on the DJI mapping database. Be familiar with your surroundings and if you start drawing a large crowd, you may want to call it a flight so you don't attract too much undue attention and get your drone confiscated by the police. Definitely steer clear of military installations, temples, and large crowds, and regard the flight ceilings.
2. You'll be able to find spare parts in these countries if you're willing to spend the time to look for them and are also in/near major cities. Bangkok has some epic malls with electronics stores aplenty, but you may not want to fly or even spend much time in the major cities with how beautiful the country is outside these megacities. In short, bring spares that you know you'll need and make sure you do have an travel charger compatible with these countries. Oh, and definitely multiple spare batteries.
3. Regarding insurance, many US based insurances will not cover overseas locations so make sure it is in your policy for outside the US--this will not only cover your drone but also--heaven forbid--any damage your drone could cause in a foreign country.
As for shooting, definitely invest in a good set of ND filters, especially if flying near/over water. They will absolutely come in handy. And if your phone screen isn't that great, a sunshade or a device that you can turn the brightness way up for those sunny days is a must. I also recommend a set of extension legs for beach landings, so either legs or a landing pad comes in handy to keep from kicking up too much sand. Have fun and enjoy!