For any South Asian country I would put my money on Sri Lanka and then Bangladesh. And this is purely based on give and take relationship, Sri Lanka has more to offer to us economically and hence would be given more importance in South Asia, then comes Bangladesh and then maybe Pakistan. I didn't include Nepal and Bhutan since they already have pretty integrated economy with India.
As for the rest of the world I would say it would either be China or Japan, both countries have been pretty close to Modi when he was/is the CM of Gujarat. So it would be natural for him to build upon that relationship and further enhance the trade deals with the two countries. Russia is a given, they have been a major ally and, have supported India through think and thin same goes for Israel. Iran is the new country in the equation, with easing of sanctions a better trade relations with Iran can be further enhanced. As for the western countries not counting Latin American countries since he will be going to Brazil for the Summit so that will give us some outlook on his policy towards that region, but as for the west I would say there is still a bit of distrust in the air, so I wouldn't expect much.