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You can drive to Prince Rupert in north British Columbia and take the Alaska Marine Hwy (Alaska ferry) to Southeastern Alaskan ports such as Ketchkan and Skagway, Alaska. That will be a shorter drive than going to Anchorage and you sail through one of the most scenic areas on earth - Inside Passage. Cruises all go throug Inside Passage. Get as close to Glacier Bay NP as possible. The only way to experience Glacier Bay though is by boat tours. Some ferry routes do go through Glacier Bay.  In my opinion, visiting Alaska without seeing tidal wave glacier is like never been there. Most of the other sceneries in Alaska you can find similar sceneries just as nice in Western Washington and British Columbia. The only way to see tidal wave glacier in Alaska is from boats. Ferries often times will stop and get close to famous tidal glaciers (not sure about the SouthEastern AK ferries).

You can also ferry hop and make multiple stops if you plan it right. However many legs of ferry ride you take you have to make sure you end at a terminal accessible by road or airplane. Skagway is one of the few places in Southeastern AK accessible by road. Ferries are not going to cheaper but you do have the flexibility of staying as many days as you like at a single location. There may not be daily ferries on many routes - you should make ferry reservations ahead of time. Keep in mind many of these Southeastern Ak terminals do not have roads to the outside world. Without a reservation and a ferry gets filled, you may be stuck for days. 

Here is the website to Ak Marine Hwy http://www.akmhs.com
Bellingham, WA on the US side is also served by Alaska ferry but that would be a much longer ferry ride.

Be sure to ask your rental car company if the contract allow you to drive to Alaska and/or into Canada. You don't want to get caught violating contract (with a long drive, your chance is bigger). Rental cars do break down (mine did during my last trip to Anchorage-thank goodness I wasn't on a gravel road).

Southern Alaska panhandle is one of the rainiest areas (also the most beautiful area) in the world. It will rain for sure almost any time of the year since it's the rainforest. That's just something you have to deal with visiting the area. Fairbanks is dry but there isn't much to see there.

If you do end up visiting the Alaska interior, don't expect to see Mt McKinley, which is only visible 20%-30% of the time, mostly in winter. I have only seen it once flying from Fairbanks. Plus, I don't believe Denali NP's shuttle is running in May, which means you have to drive on long gravel road, a violation of your rental car contract.