My 2 cents on BKK & LOS (land of smiles):
You can hit the Bangkok highlights in 2 days.
Take one morning or afternoon to see Wat Arun, Wat Pho, and The Grand Palace. The best way is to take the BTS to Taksin and then take the Chao Phraya express boat (orange line) up to stop 8. You can take a ferry across the river to Wat Arun and then come back and walk to Wat Pho and then the Grand Palace.
Go to the Jim Thompson house museum and MBK for some knock off goods shopping. They are at the same BTS stop.
If you want to buy something go to Chinatown to visit the gold shops (they are everywhere, but the best ones are in Chinatown). Thai gold is 23 Karat, so the jewelry has a deep gold color and is very malleable. I would spend money on a small gold chain over junky souvenirs.
One night go to Nana entertainment complex to visit some go-go bars. Hit Obsessions on the bottom floor if you want the Katoey experience. You could hit Soi Cowboy as an alternative, but avoid Patpong - it was bad before COVID, and I hear it's worse now.
Hit one of the many rooftop bars across Bangkok. The Sky Bar at the Lebua tower is the one from the Hangover 2, but it's always crowded since the movie came out. Personally i like Octave. Vertigo is also very popular.
As far as food, eat street food. Make sure you get Som Tam and ask them to make it Isaan style w/ the crab.
If you spend more time in Bangkok, then you can do a day trip to either Ayutthaya or The Bridge Over River Kwai.
Beyond Bangkok, Chiang Mai is nice but far (overnight train ride is the best way there). If you don't want to lose as much time traveling then look into taking a bus to Hua Hin for a laid back beach or Pattaya for a not so great beach and crazy go-go and beer bar scene that makes Bangkok seem tame. If you don't mind flying you could hit Koh Samui or Phu-ket. You should be able to get direct flights from Phu-ket to Saigon (or maybe Hanoi).
Make sure you have your onward travel out of Thailand booked before you check in to fly there. Airlines are supposed to check for this (some do a better job than others). Immigration sometimes randomly checks as well, and if you don't have onward travel booked they won't let you in. Also, make sure you have 20K Thai Baht equivalent in cash (~$600) in hand when you go through Immigration.
Outside of Thailand, I agree w/ other posts - Angkor Wat is a must see. If you don't see it this trip then you need to come back. I can't comment on Vietnam as I haven't been there. My wife spent 3 weeks there traveling around and said it was very beautiful.