Late June is a great time to go, with the longest days of the year. You'll be able to read a newspaper out on deck at 11pm with no problem.
Most ships hit the most important ports of Juneau, Skagway, Ketchikan and a ride through Glacier Bay or similar. Some ships are still going to Sitka, a port with lots of history and wonderful things to see. To me, Skagway is the absolute "don't miss" in Alaska.
Alaska is AWESOME! We were the last tour of the season in september and had a wonderful time as all the wildlife was visible. It's hot during the summer so everything "alive" disappears but in the spring and fall bears, whales, otters, seal, etc. are feeding and out in the open. Catamaran whale-watching in Juneau was awe-inspiring! Fully guided horse-back riding the original Chilkoot trail was not to be missed. Just the van ride getting to the trail was amazing. Scuba-diving was almost a religious experience!!! Who would have thought to scuba dive in Juneau but it's a rainforest! Make sure you view College Fjord and Glacier Bay national park from the best seat in the house - The Rear Hottub!!! LOL We witnessed (and videotaped) calving ice-bergs. We had a naturalist on board so everything was explained. I would go back to Alaska in a heartbeat!!! We had stunning weather with only 45 minutes of rain the entire time! We cruised Whittier Bay (Anchorage) to Vancouver. The only down side was that it was chilly so ship maintenance was "off", but the Sun Princess was also heading into San Francisco for a full re-furbish so the push wasn't on to keep her exactly "spiffy".
Alaska is almost a religious experience...I've done the inside passage 3 times and will do it again this summer.....Skagway is my favorite...The train ride and lots of historical buildings and shopping.....and you can go pan for gold if you are up to it...Happy Cruising...