Update 17 April 2019
If it is your first time you should visit the Grand Palace with the Temple of the Emerald Buddha, 500 thb. If you organize well , you can do the Grand Palace ( only open before 2 pm), Wat Po and Wat Arun in the same day.
As it is close to the famous Kao San road, some of my surfers book a dorm bed for on night (about 90 thb), so they can combine AND Kao San Road, in the evening, AND the temples in the morning.
When you stay at my place, you can go out late, but please advise me before, and please not every day!! If you have money to go out, you have money for a guesthouse too.
The Skytrain stops at midnight , reopens at 6 am, and the songteows run till about 10.00 pm.
After 10.00 pm better take a taxi, about 50 thb, or the motorcycle taxi, 30 thb.
Saturday and Sunday, you can visit the weekend market at Chatuchak, close to the BTS station of Moochit. Chatuchak counts over 15.000 shops!!! And in the weekend you also can visit a floating market!
http://www.theworlds50best.com/blog/News/50-best-destinations-an-insider-guide-to-bangkok.html
What to visit outside Bangkok?
The closest beaches are 3 hours by minivan from Bangkok, Hua Hin is my favorite, but both Ko Lan and Ko Samet (Ko= island) are nice too .
If you want to go further, in the winter go south, in the summer go north, to avoid too much rain.
There are buses (3 main bus terminals in Bangkok), trains (Central Station and Southern station) and cheap airlines for domestic travel in Thailand, and you also can travel by mini-van.
Also visit the video " 25 things to do in Bangkok"
https://www.youtube.com/watch?v=-OtmiE_6nqc