Anchorage is about 75 miles from Seward and 65 miles from Whittier, the two ports Alaska cruise ships depart from.
Transfers from the cruise lines will run you about $55pp, one way to or from Whittier or Seward and take about 2 hours.
You can take the Alaska railroad from Anchorage to Seward for a cost of $46pp. The train departs from Anchorage at 6:45am and arrives into Seward at 11:05am. The return train leaves Seward at 6pm and gets into Anchorage at 10:15pm
Another option is the Alaska Cruise Transportation. They offer a 3 hour ride from Anchorage from Seward/Whittier or reverse. Their rates start at $25pp.
They also offer several other options including tours with guides that can last as long as 8 hours. See all of their options at http://alaskacruisetransfer.com/
Hotels in Anchorage can be pricey in the summer. Limited options means finding an interline discount can be difficult. Often you might have to settle for any room you can find. Downtown Anchorage is relatively small, so if you stay there you will find it easy to get around and see what downtown Anchorage has to offer.