Alaska is a little more expensive on average due to a short season and if you need air fare from the East Coast this will be additional ($700pp). I would say an outside cabin on HAL. Princess, RCI ships would be about $1500 pp plus air on up for a 7 night cruise only inc. port & taxes. (This may be a little on the high side, too as I have not looked at an Alaska brochure in years.) Prices have not gone up due to the increase of ships sailing the routes. There also should be some good sales soon. Travel anytime from mid-June to end of August, too.
I would give a T/A a call. Right now there are some great prices on Celebrity and Princess Alaska cruises in May and September. The airfare may be a little high if you are coming from the Central or Eastern U.S. As Nana said, about $700 per person.
You can also put a inquiry in "Bargain Finder" here on the CruiseMates website. There are balcony cabins available for under $1,500 for May and September cruises. It doesn't cost anything to ask.
Ways to keep costs down is to deal with a large cruise only discounter, I would also not hesistate to book a cheap inside cabin, the last few years I have sailed about $500 doing this on a 7 day cruise. I would avoid mid to late Sept though for a first timer- short days- dark by 7pm, cold- 40-50's and good chance of rain. Much better weather late August- good rates as well.
I paid $1700 for the last week in June aboard the Mercury. This includes cruise,air from east coast and travel insurance. We are on the Penthouse deck but have an inside cabin. I just saw on one of the sites a price of 999 w/air from the east coast.
If you want more info email me.