Pack layers of clothes, as temperatures can be in the 50s or the 80s, or anywhere in between. Casual clothes are best: jeans, sweatshirts, etc. Bring gloves and a hat or earmuffs if your ears are sensitive to cold - you may want to spend lots of time on deck, as the scenery is so incredible. I'd recommend having 2 pairs of walking shoes (sneakers are fine) in case one gets wet; some areas of southeast Alaska can be rainy. And bring rain gear - ponchos or slickers will be great, especially with hoods.
There are lots of activities on board, and just walking around the little Alaskan towns can be fun in itself. Check on Google for specific information about each port you'll visit - most have museums and other attractions. And check portreviews.com for suggestions of what to do as well. Have a great time!!