How cheap do you want to go? In BKK there are accommodations to fit every budget. How down market do you want to go? Back-backer guest house with fan and shared bathroom? Do you want to stay near the airport? I'd not suggest that option. Do you want to be in town? Near the river? Near the Hilton? If you want cheap, grab an airport taxi and ask the driver for a cheap hotel.

I suggest you contact the Hilton and let them know you'll arrive after 1 or 2 AM. Try and negotiate a rate for an early arrival or checkin. It is hot as heck in BKK now. Unless you speak Thai you will have a language barrier to overcome. You'll arrive fatigued, add the heat and the excitement of an Asian city and you might be on sensory over load. You will appreciate the calm oasis of the Hilton.

It would be comforting to grab a taxi to the Hilton and arrive to the friendly welcome of a English speaking staff, cordial staff, a nicely appointed air conditioned room. Sleep late or go out and see what is buzzing in Bangkok at night. Sleep in, have the breakfast buffet, enjoy life. My own view would be to avoid the hassle of moving from one hotel to another to try and save a bit.