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It is said that Buddha has divine eye (ability to see who're capable of realizing liberation) and psychic power.
Is there any account in pali canon in which Buddha sees someone who could realize nibbana and travels outside India to teach? It seems to me there would always be someone outside or far from where Buddha dwells who can see Dhamma?
The Buddha visited Sri Lanka on three different occasions. His first visit was to Mahiyangana; the second to Nagadipa, and the third was to Kalyani (Kelani). On these three occasions he stayed at sixteen specific locations and meditated by himself or with his disciple monks. For that reason, those places have come to be regarded as highly sacred. They are called the Solosmasthana.
Apart from that, the Buddha visited the Thawthisa heaven, seven years after his enlightenment to preach the Abhidhamma to his former mother and the other Devas and Brahmas. He spent three months there.
He also visited a country called Sunaparanta with four hundred and ninety nine arahants, including venerable Kundadhana and venerable Ananda.
Any answer to this question would be purely conjecture. We don't have any secular evidence to suggest one way or the other with any certainty.
The mythology spoken of above can be taken or left, depending on what brand of Buddhism you follow. Zen would not, for example, give two shakes about anything The Buddha did after death, if, indeed, it was possible he could. Tibetan Buddhism has a huge mythology built up around things like this, and mystical events that are quite detailed. Pureland Buddhism would tell you you simply can't become enlightened in this lifetime, and that you must say the Mantra of Amitabha Buddha to become enlightened in the Pureland after death.
It all depends on the flavor of ideology you are involved in.
At its core, Buddhism doesn't care. :-)
Now if you are asking this question in an attempt to get at some historical figure you think that Siddhartha may have taught, can you tell us who that might be?
