We were on an Alaska cruise last year during the first week of July. We had great weather half the time, and luckily when we needed it - cruising the glacier and helicopter ride/dogsledding on Mendenhall Glacier. The week after us had beautiful weather. June through August is probably your best bet. We cruised with Celebrity. It was our 20th anniversary so we splurged on a Junior Suite - really just a larger room, but you get butler service and preference for tenders. I would definitely recommend Celebrity - fantastic trip and unbelievable scenery, good food, excellent to fair stage shows, and superior lounge acts. We saved a bit of money doing independent excursions rather than the cruise line's. I found great info on excursions online and all of ours were very well run and enjoyable. Hope this helps.