The weather can vary. July is likely to be the warmest month, but there can be some very nice weather in June and August - also in May and September, if you're lucky. If you are planning a cruisetour (adding on a tour before or after your cruise into the interior of Alaska, to visit Denali National Park, for example), be aware that late June through early August are the buggiest months. Not a huge deal in southeast Alaska, along the Inside Passage, but it could be a bit of a problem in Denali.
Also note, cruise and tour fares are higher in June, July and August; you can save by booking a May or September trip.