If you entered on an actual Tourist Visa which you paid before you flew into Thailand and were stamped for 60days, you are going to go to Chaengwattana Immigration office, Government Complex Building B.
You will go here.
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If you entered Thailand without purchasing a visa prior to your travel to Thailand, you are going to go to IT Square Laksi Plaza temporary office, just next to Lak Si station on SRT Dark Red Line.
You will go here.
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And you can book online here
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General information for tourism extension is attached