You can easily get a bus from Bangkok to Chiang Mai and return. You can book in any travel agency. Prices range from 150 Baht to 300 Baht. Do some shopping and get the lowest price. Do not get ripped off!
I wish I remembered our drivers name because he turned out to be a very kind man who took joy in showing us around Chiang Mai and its environs. He arranged several day trips for us and seemed to go above and beyond what you'd expect from an ordinary driver. Our hotel sent this driver to us to meet us at the airport and later we arranged to have him as our primary mode of transport in and around Chiang Mai. For $20 a day (divided between 5 of us) we got an air conditioned mini van and a driver that happily took us anywhere. The only problem was that he didn't speak english (not a problem considering we are in Thailand) but we were lucky enough that my wife is a Thai native and easily communicated with him. He made our stay there much easier! We hired our driver through the Lanna Resort and then arranged a deal with him on the side. If the resort gets in on the action then you'll pay more.
The most common public transportation is "song thaew" which means the Red Taxi. Song Thaew is a pickup truck converted for carrying passengers and some cargo. These vehicles are regulated and licensed by the government. In Chiang Mai, red song thaews roam the city and are free to travel anywhere. Simply wave your hand, stop one, and ask told the driver where you ant to go before boarding. Fare within the city is nomally 10 Baht, to airport 20 Bhat. Prices negotiable for longer distances.
To get to Chiang Mai is easy, very easy. You can go there by bus, train or plane. By bus, you can take the bus at the northern bus terminal. It takes 10 hours to get from Bangkok to Chiang Mai. By train, you take the train at The Central Station (Hua Lampong). If you want to go by plane, it will take only 1 hour to get there.
There are some buses and bus tours in Chiang Mai and around. If you are not into driving yourself or pay for taxi, I guess such is also an option.
You'll see lot of big red taxis like this. Very usefull if you're a big group (or with lugguages) and you'll be perhaps with other tai people inside. Don't forget to negociate.
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