We went in late May for our Alaska cruise in 2014. We were fortunate with very good weather. Layering is the key. Be prepared to keep warm and for wetness. You just never know how the weather is going to be. You have long days, but it will get dark around 11:00 PM.
It is early in the season so you won't see many (if any at all) bears since the salmon aren't running yet. However, it is prime whale watching time. We did private tours in all but Ketchikan. My trip report below can give you an idea of how Alaska will be at the end of May.