Khao Yai is located around 150 km from Bangkok. It is without a doubt Thailands most popular national park, and as such is to be avoided like the plague on high days and holidays. Khao Yai camping is very pleasant sometimes, and horrible at weekends.
You can enter the park from the south, via Prachinburi or from the north via Pak Chong. There are some lovely waterfalls in the park, along well trodden trails, and also some good campsites, which do get very crowded at weekends.
I must admit to having a love hate relationship with Khao Yai. It does have a slight feeling of being a zoo, come amusement park, but there are big animals here, including elephants and possibly still some tigers. The campsites are big and well maintained and if you do not find yourself camping 10 feet from your neighbour in Bangkok, very pleasant. The usual powers that be in Thailand have eaten their fill from the national park over the years, so some areas are more like golf courses, but what do you expect when pigs have their snout in the trough? Despite that, some of the trails in the park are really lovely, and you can feel quite alone, but do expect leeches (loads of them during the wet season)
There is a well organised visitor centre. I will not go into detail about campsites, both are big with reasonably clean bathrooms/toilets. There are also several resorts around the park that would be amenable to you pitching a tent. My undisputed favourite is Kamol’s Farm https://www.facebook.com/kamolfarm.khaoyai which has rustic bungalows in a beautiful setting. I believe you could also ask them if you can pitch a tent there, but you would have to make it worth their while. It is about 40 kms from the park entrance near Muak Lek. On crowded weekends, that may be a better way to go.
What I would say, is that you should not let Khao Yai camping be your only experience of camping in Thailand. It is popular in the way that malls like Central world are popular; probably because they have the best merchandise selection, and all your friends will like you on facebook for having “been” there. You can dig deeper, but not at weekends, and find a lovely well kept national park, but you do have to dig deep.
Here is a link with lots of detail
As usual, this website is exceptionally useful.