It is easy to move in the Bangkok, there are amny possibilities (tuktuk, taxis, buses, metro ...) and to get out of Bangkok there are also many ways too buses or taxis while ago but don't forget the train! Inexpensive, you will discover the countryside around Bangkok.
And 80 km from the city is the site Ayutthaya I urge you to visit. Go by train, spend the day there, it will be one of the finest you will have in Thailand (if you love visiting)!

Station Bangkok
 The Bangkok Railway Station
Country side in Thai train