Take the MRT metro in Bangkok
Take the MRT metro in Bangkok and go easy arround the City. This also connects with the Skytrain. It's a easy transport way and very cheap. It's very clean and you can really get arround the city.
You can read more about MRT in Bangkok on transit Bangkok. It is easy and self service most of the time. There is security check going to the metro, but they never look in bags when you are turist. So go sightseeing with the public transportation in Bangkok and connect with Skytrain BTS so that you can see even more.