Are you going alone? Will you have a car? What date and time do you arrive & what date and time do you depart? Do you have 7 days (i.e. 6 nights)? or 7 nights (i.e. 8 days)? Big difference.
First of all, do not plan on spending all 7 days in Anchorage. Alaska is just too big to do "day trips" from Anchorage.
Let's assume you have 7 days (6 nights) and that your flight departs Anchorage in the evening of Day 7 like many do. Maybe something like this:
Day 1 arrive Anchorage
Day 2 drive to Whittier, take Prince William Sound glacier cruise, drive afterward to Seward (1+ hours to Whittier, 2 hours from Whittier tunnel to Seward)
Day 3 do a combo fishing/Kenai Fjords trip, maybe with Saltwater Lodge. This will allow you to also see marine wildlife
Day 4 visit Exit Glacier and hike to the toe of the glacier, then drive to Talkeetna (about 5+ hours depending on traffic, road construction, etc). If interested, book flightseeing for this evening - very popular to do flightseeing tours from Talkeetna (summit flights, flights with glacier landings, etc)
Day 5 morning back up for flightseeing if canceled last night, then drive from Talkeetna to Denali. Entrance-area activities like visitor center film and exhibits, sleddog demo, drive the first 15 miles of the park road, the Savage River Loop hike (2 miles round trip, easy level hike)
Day 6 book a shuttle bus to Wonder Lake, but if the weather is such that you can't see Mt. McKinley then get off at Eielson. Return on a different bus and get off the bus for a nice hike on the tundra. Ask the rangers at Eielson or the bus driver for ideas. The area between Eielson and Toklat is great for first-time hikers - low tundra, good visibility, etc.
Day 7 drive to Anchorage, fly back home later in the day
If you have an extra night, you could spend it either in Seward or in Denali. With your wildlife/bear and hiking interests, I would spend another day in Denali and book a second shuttle bus to Wonder Lake. That would give you more chances to see bears. The area between Toklat and Eielson is prime bear habitat in Denali NP.