Literally too much stuff to write about Bangkok. Here are the bare minimum highlights.
Ayutthaya is one of my favorite ancient cities and its about 1.5-2 hours from Bangkok. If you want a private car, you can book with Bangkok Shuttle directly online and it is 3,800 baht (about 100 USD) for the car. You can tell them to drop you off at Wat Mahathat and then pick up at Wat Chaiwatharam. When you get there you can just a TukTuk for a 300-400 baht to drive you around the grounds (they usually know what order to take you to the temples). OR you can book a tour with one of these companies. It's honestly about the same cost.
Banyan Tree is the best place for dinner-- the view is incredible, but it's very nice so make sure to make a reservation and dress appropriately. You can go for a cup of tea and beer at the end of the night as well.
The weekend market and Bangkok's Grand Palace are both very impressive. Traffic in Bangkok is VERY bad, it's always better to take tuktuks (they charge 100-300 baht) because if you take a care you will be stuck in traffic FOREVER (add 30 min for every trip).