That's the place. There are two terminals when you arrive... one on the left, one on the right. Yours is the one on the right (evident by all the green buses parked there ;))
At Myanmar immigration you will be offered the option to shop in Myanmar or just go back to Thailand. With your 2 hour window, I would just go back, grab lunch and then catch the song theaw to the bus station. Sometimes when there are groups crossing, there can be a backup of people getting into Thailand.
Be sure you go to the correct bus station in Chiang Mai (Arcade out towards Central Festival). Have a good trip!
Book green bus online (get a VIP seat...first 4 rows) to Mae Sai. Choose to pay at 7-11 and just take the code to any 7-11 where you pay and your receipt is your ticket.
Good plan. Lots of great places to explore that are so close... Angkor Wat in Cambodia, Malaka Malaysia, Bali, Luang Prabang Laos, Ho Chi Min Vietnam (sidenote, out of all of those... only Malaysia and Bali are free visas). Check out here for some cheap flights:
Then do as Robert said... enter on 60 day SETV, extend for 30 days at immigration (1900 baht) and then again near the end apply for extension and they will deny it but give you 7 days (1900 baht).
Reason I recommend the METV is that you can easily spend half the day at immigration for each extension and you will be spending 4800 baht on visa and extensions. With the METV, you enter for 60 days and then just take a 'border run' (step over the border stamp out, stamp in) to start another 60 days.
Now.....you mention you're staying in Koh Phangan? Is that for the entire trip? Because extensions and/or visa runs are going to be a pain in the butt as there is no immigration office on the island. You would have to go to Koh Samui each time.
Do you already have the 60 day single entry tourist visa? If not, apply for the 6 month multi entry tourist visa which will give you 60 days per entry. Otherwise, enter on SETV for 60 days and then plan a
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day trip to another country and return on exempt entry (free) to get you 30 days more.