The Ancient City is huge and incredibly beautiful (rent a bike or golf cart, you will need it), it's a great place to enjoy all the beautiful structures surrounded by a very peaceful ambient! The only note: give the elephants to an elephant sanctuary, they looked well treated but there's no need for them to be there in a not really large space, the structures and the entire place are beautiful enough.
The Erawan Museum is stunning! Visit and admire the main building, it is gourgeous, but don't forget to explore the garden and the whole space, it is full of wonderful peaceful corners, waterfalls and places to just enjoy the scenery. The security guard in the main building was wonderful, he noticed we were having trouble taking some photos and stepped up to help us take some photos that were honestly of the quality of a professional photoshoot! Thank you so much!
Regarding Headout, we are very grateful to have found this tickets they were half the price the tickets at the door and we were able to buy them while on our way to Ancient City, by the time we arrived we already had the tickets in our email. We had no issues so it was a wonderful experience!