Should I speak in the the dialect of the place I am visiting, or speak in my original dialect wherever I am, with pride in my homeland and origin?

There is no blame upon you for speaking in your country's dialect, and you are not religiously obligated to speak in any other way. It has been reported that the Prophet (peace be upon him) used to address each people in their own dialect, thanks to the knowledge of Arabic tongues that Allah had bestowed upon him, as mentioned by Qadi Iyad in "Al-Shifa'," citing examples of his speech (peace be upon him) with various tribes.