During our cruise/land tour we have a free day in Girdwood (staying at Hotel Alyeska). Any suggestions on what we should not miss. The tours gives us lots of options but we are open to maybe take off and rent a car or something different other than a tour.

When is your trip? Where are you departing from; Anchorage, Seward or Whittier? Car rentals are not much of an option for anywhere other than where is an airport.

Sorry, you have no car rental options here. Probably one of the best tours in this area is a PWS boat tour, with getting to Esther Passage the best routing. Would have to book this with some sort of transportation package through your cruisetour/lodge.

We stayed in Girdwood at Alyeska Resort. There is a lot to do there. For starters, you shouldn't miss the Winner Creek Trail. Good hike with a unique way to cross the creek. You can ride the gondola to the top of the mountain. You can arrange a guided hike on the glacier there. There is also paragliding off the top. There is a very good casual restaurant at the top, and probably one of the best restaurants in Alaska can be found at the top, 7 Glaciers. There is a good Japanese in the hotel at the bottom. A really good Cajun place is not far away. I am blank on the name right now.
You might want to consider taking a helicopter/glacier landing/dog sledding tour.

We did the heli/dogsled tour, and also did the glacier hike.

I second the Winner Creek hike. You an also rent bikes at the resort and go for a beautiful bike ride. Our family did the Alpine Air dogsled experience on the glacier and absolutely loved it. It is only 1/2 day and can be booked through the Alyeska concierge. We did the 10:15 tour, arrived back for lunch at the hotel and then hiked in the afternoon. There is rafting not too far from the hotel (45 min). Ask the concierge for the activities guide - they can email it to you. The cajun restaurant is the Double Musky - great ambiance, lots of character. Food good but not the best that we had on our trip- though alot of people really love it (don't miss the pepper steak). If you take have a dinner reservation at the Seven Glaciers you don't have to pay the tram, it is included (around $18 each I think).

Forgot to mention that you do not need a car for the Alpine Air dogsled/heli trip - they pick you up at the hotel.