I was wondering if it's possible to go to an Apple Store overseas (none in my country) and hand over my iPad for store credit in order to upgrade?
iPad (3rd gen) Wi-Fi + Cellular, iOS 9.3.2
That would depend entirely on what country you intend to go to. However, you would probably fair much better ($ wise) to sell the device your self.
Generally speaking Apple does offer a Recycling Program in some countries. most notably the U.S. where in you can recycle your old device and get a gift card with the value of the device as determined by them for use in an Apple Store.
Whether you can do this would depend on the country you intend on going to.
As has been pointed out, you are very likely to get more money for it if you sell it outright yourself, than whatever the recycling program might give you for it.
If you decide to sell you old iPad as others have recommended, be sure to read this Apple article:
What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support
and apply the steps shown. Otherwise the iPad will be useless to the buyer and they may come looking for you!
Thank you for all your responses! I had a thought about taking it to an Apple Store in Miami but maybe I'll sell it myself. I'll take a look at that Support article. Cheers!
http://www.apple.com/recycling/
Has information and a valuator for your device.
Other retailers will also give you store credit for selling your device to them. I use Best Buy, but Amazon also has a program and there are others.
The article below has info on how to wipe your device and remove it from your Apple ID when you sell it
What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support
Upgrading iPad
