In OTL, Shogun Toyotomi Hideyoshi launched two invasions of Korea in 1592 and 1597, sparking off the Imjin Wars which both ended in the intervention of the Ming Dynasty on behalf of Joseon and Japanese withdrawal from the peninsula. On hindsight, his goal of conquering China via Korea looks downright insane, given the disparity of their strength at the time. But he did set other, more realistic targets at the time, such as the Ryukyus, Luzon and Taiwan.
The question is, what if he had organized an expedition elsewhere, instead of Korea. How successful or dismal it would it have ended and what would be the effect of his invasion in the East Asian region. Besides the ones listed above, are there any other areas of expansion he could have taken, such as Hokkaido?
As far as I can tell, any invasion that attracts the attention of a larger power would not end well. The Ming would certainly resist an outright invasion of the Ryukyus (just as they did in Korea), though I'm not too sure about Taiwan, being mostly inhabited by aboriginals and malaria-carrying mozzies. Luzon is probably out too, being a Spanish possession. Hokkaido seems like the best possible target, though that would depend on how well or badly the Ainu could hold them off. Overall, Hideyoshi didn't have that many options to play with, given the limits of his naval reach and certainly with other, greater powers around.