My parents, as well as my husband and I, will be arriving in Anchorage on Wed. May 25th around 4:30pm, and will be leaving very early Friday morning. We will take a train to Seward, where we will start a cruise that day on Celebrity (Seward to Vancouver).
That leaves a with 1 full day (Thursday) in Anchorage. I need recommendations for that day. Should we just walk around downtown, or should we rent a car and do a driving tour.
If we do not rent a car, any recommendations on hotel and their locations?

I'd go for walking around downtown and shopping. Anchorage has some of the BEST selection of Made in Alaska gifts and souveniers in the state! The whole area is really cute and very pedestrian-friendly. The Alaska Art & History museum downtown is very good to give you an overview of the state.

Eat at least one meal at the Glacier Bay Brewhouse!!
Also, the Downtown Diner has its famous sourdough pancakes and reindeer sausages.

If this is your only time in Alaska apart from the cruise portion, consider renting a car for a day. Drive down to Girdwood/Portage, stopping along the way and taking in the sights.

Have lunch in Girdwood, look for Dall sheep and belugas along Turnagain Arm, ride the tram up Mount Alyeska. That should take up half a day (If you go in the evening, have dinner at the Double Musky.)

Yes, you'll see some of that territory whizzing by on the train, but this is a great stretch to stop, poke around and see things that so many cruisers unfortunately miss.

You can spend the other half of your day in downtown Anchorage.

IF this is a rare Alaska tour, then I would rent a ONE way car and get to Seward the night before and take an early Kenai Fjords tour your day of cruising. Far FAR superior to any close up glacier and wildlife viewing you will get from your ship. Request the Anchorage visitor guide, www.anchorage.net nice walking tour map inclosed. Make the most of your too short time.

If you decide to stay in Anchorage, check out the show at the Fly By Night. I guarantee you won't be disappointed. It's hilarious!

If the weather is nice, you could rent bikes or just walk part of the Tony Knowles Trail along the water.