Thammasat isn't bribable. Thaksin found that out when he offer 1,000,000 to the Faculty of Political Science to admit his son. They told him quite bluntly that they don't do that. (He did get him into the Faculty of Engineering, which he hated and dropped out of in his first year.) But Chula and Thammasat are the hardest to get into academically. An exception are the international programmes. One student told me she enrolled in the SE Asian Studies programme because it was the only way she could get into Thammasat. Some classes are in English, others in Thai, and the students have to choose two other Asian languages to learn. (Most take Lao and indonesian, because they are easy.) The students also spend a summer in the countries whose language they've studied. It seems like a fun programme to me. (I taught them several times.) It is good preparation for a job, since being able to speak 3 Southeast Asian languages as well as English should be worth quite a bit in today's ASEAN common market.
TU also has a British American Studies programme. This gets you around the nationwide university entrance exam too. (It used to take about 97% to get into Chula, and 95% for Thammasat. I don't know if it's still that hard, since the government keeps playing with the entrance exams.)
My wife's niece went to Mae Fah Luang University, which is a government supported university. The reason she chose it was because it's fairly new and not many Bangkok students want to go up to Chiang Rai, so the competition is low. (She's also happens to be from Chiang Rai.) It has a beautiful campus and I'd rate it well above the rachapats, which are really the old teacher colleges dumbed down. All of the retired teacher college archans I know tell me they're disappointed at what the rachapats have turned into.
Chulalongkorn does hold about 30 seats each year for the children of the posh or powerful. That's how Thaksin's daughter got into Chula, even though her score on the nationwide entrance exam was only about 83%. A colleague told me he was quite angry when he discovered his grades had been altered at Chula to raise them for the students from prominent families. (One girl waied him and thanked him for her grade. He said, "I gave her a C.") Chula panders to the rich and powerful. Thammasat doesn't, at least not to the same degree.
My Thammasat students told me that everyone usually picked Kasetsart as their fourth (and last) choice when they took the entrance exam. It's not as prestigious as the top three (Chula, Thammasat, Mahidol), but it's nevertheless a good university and quite respectable.
Assumption is probably the top private uni, though the students are unhappy that they don't receive their degrees from a royal family member. Instead, they receive it from a Catholic brother from India.
A happy childhood... is the worst possible preparation for life. - Kinky Friedman