I've traveled to over 40 countries in the past 5 years, so although my long-term relationship experience is quite limited (it's almost Valentine's Day so I'd rather not dwell on that part), I still find going out with locals to be one of the most interesting parts of my experiences overseas.
Make sure you have a distinct social circle so if things go south, you aren't alone and having to make a tough choice between all of your new friends or your former love interest.
Also, his or her family and other close friends may not speak English, so speaking a basic level of the language will help bridge some important cultural and linguistic gaps.
In any culture, knowing the people around your boyfriend or girlfriend is an essential part of the relationship.
In many countries, it improves a person's social status to be seen with a foreigner, so don't eliminate the possibility that your exotic looks, accent, and nationality play a role in your relationship to some extent.
It can be tempting to have a native boyfriend or girlfriend so you have someone to show you around town and teach you the local language, but in the end it's just not nice.