IF you entered Thailand on visa-exempt for 30 days, without purchasing an actual tourist visa, you are going to go to IT Square Laksi Plaza temporary office, just next to Lak Si station of SRT Dark Red Line.
You will go here.
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IF you applied for and got a Tourist Visa before you travelled to Thailand, entered on that visa being stamped for 60 days, you are going to go to Chaengwattana Immigration office, Government Complex Building B.
You will go here.
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BUT, if you are on any other entry type (visa-waiver, visa-on-arrival, non-immigrant type, etc), you cannot apply for a tourism extension.
You can book online for those Bangkok offices.
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Here is the general information for a tourist extension.