Can I extend my 45-day visa in Hua Hin instead of Bangkok?

The user is considering whether to extend their 45-day visa in Hua Hin instead of Bangkok. A comment suggests that it is permissible to choose either location but stresses the importance of having a TM30 filed with the Thai Immigration office where the extension application is made. The extension would add 30 days to the current end date of the stamped permission to stay.