There's a theory that in Jesus's 'lost years' (the time of his young life that's not discussed in the Bible) he travelled east to India, and maybe other places, and learned a lot of Hindu/Buddhist/whatever teachings, which would later help to inform his own philosophy.
Is there any solid evidence for this? Or is it all merely speculation?
In short no, there's no evidence that Jesus traveled to India or engaged with Hindu or Buddhist though.
Here's a comment thread in which I address some of the India question directly.
Well that actually brings up the "three wise men from the east" Upon Jesus birth. Is that a fable? Is there an early connection to the east here.?
Outside of the Gospels, which were not written during Jesus' lifetime, there's no solid evidence for the historical existence of Jesus. Sources outside the bible do attest to the existence of other individuals who are part of the Jesus story, such as King Herod and Pontius Pilate, but no outside source provides reliable evidence for Jesus the Nazarene, much less where he may have traveled during the years the bible skips over.