Assuming HUGE advancements are made and you can somehow travel the universal speed limit of light, it's gonna take you more than a thousand long lifetimes to travel across the Milky Way.
While statistical projections point out that there must be other complex life out there, I don't believe it. The earth is not a common rock in a common star system, in a common galaxy. The balance of light, minerals, orbital planets and other necessities for life to form on earth is so incredibly rare, that it is absolutely unimaginable of all the things that contribute to it. I think that there is probably a microbial life form in many places across the universe, but complex life? It's rare.