Sounds like you have a great chance to see quite a bit of Anchorage. But personally I would not spend 3 nights just to see Anchorage. There is too much other great stuff in the vicinity to see/do. Where does your cruise start from? If Whittier, I would go early enough before the cruise to take a Prince William Sound tour then board your ship. You will get much closer to glaciers on this small boat tour than you will on the cruise ship.
If your cruise departs from Seward, that nice town deserves two days/one night - arrive one day, see the Sealife Center and Exit Glacier, the next day take a 6 hour Kenai Fjords NP boat tour then board your ship.
Having been to Alaska over a dozen times, it was only last May that I actually spent two nights in the city. There is indeed lots to offer but I just think the surrounding area has a lot too. With a car rental for a day you can get to the Matsu Valley (places like Independence Mine, Wasilla, Palmer, Eagle River) and even Talkeetna.
But you did say you have another 10 days in the interior so perhaps you are getting to some or all of these places anyway.
For things to do in Anchorage, here is a list from a poster on Trip Advisor with the screen name Places. She has been to Alaska many times and compiled this list after someone told her "There is nothing to do in Anchorage."
John
1. Log Cabin Visitors Center on 4th Avenue and F Street - Start your visit here
www.anchorage.net
2. Anchorage Museum of History and Art
www.anchoragemuseum.org
3. Alaska Native Heritage Center
www.alaskanative.net
4. Resolution Point and Captain Cook Monument with views of Cook Inlet and Mt. McKinley
5. Earthquake Park, West on Northern Lights Boulevard near Aircraft Drive
6. Elmendorf State Hatchery
http://www.sf.adfg.state.ak.us/state...y/hatchery.cfm
7. Fort Richardson Hatchery
http://www.sf.adfg.state.ak.us/state...y/hatchery.cfm
8. Far North Bicentennial Park off Tudor and Abbott Roads with miles of trails for hiking and biking
9. Kincaid Park on West end of Raspberry Road with 35 miles of hiking and biking trails
www.muni.org/parks/index.cfm
10. Oomingmak Shop - Musk Ox wool hand knitted masterpieces by Native Alaskans
www.qiviut.com
11. Ulu Factory at 211 W. Ship Creek Avenue
12. Music in the Park every Wednesday and Friday at noon, 4th Avenue and E Street
www.anchoragedowntown.org
13. Summer concerts at Town Square on Thursday 5-8 PM
www.anchoragedowntown.org
14. Music and Dance on Saturday at 2 PM at Peratrovich Park, 4th Avenue and E Street
www.anchoragedowntown.org
15. Wild Salmon on Parade throughout downtown. See map on
www.anchorage.net/salmon
16. Theater Thursday at noon in Peratrovich Park, 4th Avenue and E Street
www.anchoragedowntown.org
17. Ship Creek Center at 4th Avenue and C Street with exhibits and free performances
www.shipcreekcenter.com
18. Ship Creek near railroad tracks north of 1st Avenue where city anglers congregate to catch salmon
19. Segway Tours of Anchorage at 630 W 4th Avenue #441-1124
20. Alaska Experience Center
www.alaskaexperiencetheatre.com
21. Alaska Public Lands Information Center at 605 W. 4th Avenue
with fascinating exhibits
www.nps.gov/aplic
22. Anchorage City Trolley Tours start at 612 W. 4th Street between 9AM and 6 PM
23. Russian Orthodox Museum at 605 A Street
24. Oscar Anderson House Museum at 420 M Street open between noon and 5 PM
25. Play tennis, volleyballs, softball at Delaney Park Strip located between 9th and 10th Avenues and A& P Streets.
26. Aurora-Alaska Great Northern Lights
www.thealaskacollection.com
27. Cyrano’s Playhouse
www.cyranos.org
28. 4th Avenue Theater Building at 630 W. 4th Avenue that survived the 1964 earthquake and is listed on National Register of Historic Places
29. Wendler Building at 4th Avenue and D street is also on National Register of Historic Places
30. Iditarod Race starts at Wendler Building at 4th Avenue and D Street
31. Bronze statue of Balto, famous dog, located in front of the Wendler Building
32. Town Square Park located between 5th and 6th Avenues and E and F Streets with gorgeous flowers and Whaling Wall painted by artist Wyland
33. Alaska Botanical Garden at Tudor and Campbell Airstrip Road
www.alaskabg.org
34. Imaginarium Science Discovery Center
www.imaginarium.com
35. Alaska Aviation Heritage Museum
www.alaskaairmuseum.org
36. Alaska Heritage Museum at Well Fargo at 301 W Northern Lights Boulevard #265-2834
37. Alaska Museum of Natural History
www.alaskamuseum.org
38. Alaska Railroad Depot with many fascinating historical photos
www.alaskarairoad.com
39. Alaska State Troopers Museum
www.alaskatroopermuseum.com
40. Anchorage Market on 3rd Avenue and E Street during summer weekends
www.anchoragemarkets.com
41. Zoo
www.alaskazoo.org
42. Surfing on a bore tide south of Bird Point along Seward Highway
43. University of Alaska Anchorage, visit bookstore for nice sweatshirts and other gifts
www.uaabookstore.uaaa.alaska.edu
44. Visit any of 150 city parks right in Anchorage
45. Anchorage Symphony Orchestra
www.anchoragesymphony.org
46. Tony Knowles Coastal Trail ideal for biking, hiking and walking
47. Visit bicycle rental shop at 4th Avenue between C&D streets
www.alaska-bike-rentals.com
48. Go biking on Powerline Pass, to get there follow O’Malley Road and Upper Hoffman
49. Attend Greek Festival in August
50. Take a drive south along Seward Highway for many scenic stops and to visit Girdwood for outdoor activities
51. Run Mayor’s Marathon in June
52. Go to AWAIC (Abused Women’s Aid in Crisis) Summer Solstice Festival
www.awaic.org
53. Use trailhead at Glen Alps to hike to Flattop Mountain and Little O’Malley Peak ($5.00 parking fee)
54. Use trailhead at Prospect Heights to hike to Wolverine Peak and Near Point ($5.00 parking fee)
55. Use Upper Hoffman trailhead for hikes to Powerline Pass and Little O’Malley Peak ($5.00 parking fee)
56. Use Eklutna trailhead for hikes to Twin Peaks and Bold Ridge trails ($5.00 parking fee)
57. Use Eagle River Nature Center to access Crow Pass, Albert Loop and Dew Mound trails ($5.00 parking fee)
58. Go bird watching to Potter Marsh on Seward Highway
59. Watch ducks on Goose Lake near UAA
60. Play 18 holes at O’Malley Golf Course
61. H2Oasis Indoor Water Park- great place to take kids of any age
62. Alaska Statehood Monument at 2nd Avenue and E Street
63. Fire Department Museum at 100 E. 4th Avenue