I traveled on the NCL Spirit to Alaska last year from Seattle.... The Sun is a very similar ship with a similar weekly cruise out of Vancouver..... When I cruised in July, the weather was 50-80 degrees F..... Therefore the mornings can be somewhat cooler than you might expect for June, so bring at least a light coat / windbreaker or sweater.....I would do both, since the weather might be colder and you could wear both in layers...... You won't need a heavy coat, so leave it at home..... On some days it was warm enough in the afternoon to enjoy a swim in the pool.....
There is a bear cave tour at Ketchikan, and you might see a bear with a train/hike tour at Skagway.... I saw many whales and seals on our trip, not to mention bald eagles.... The one thing I didn't see was a bear.... Oh, there are stuffed bears at the dock in Ketchikan and at the tram at Juneau....
You'll see snow covered mountains along the entire Inside Passage. You'll also have the opportunity to tour a glacier.... and see hanging glaciers on top of some mountains..... Everyone in America should do at least one Alaskan vacation..... Its a bigger plus being from Europe, probably similar to a Norwegian coast vacation.... something I would like to do soon.....
Lots of wildlife to see, the area is so naturally beautiful...... I enjoyed just sittiing out on my balcony watching for eagles, whales, seals, and otters.....
I suggest you surf the ncl website and the ship-technology website for more information.....Vacations to go also has a nice website with lots of information..... The Sun's sister ship is the Sky, which is now the Pride of Aloha.....