Neel,
As far as the Spenard Hostel in Anchorage probably not the best stay...I personally am uncomfortable with Spenard, but I don't really know of any more in Anchorage, I think there is one downtown. I'm sure the Seward one isn't as bad because of the town size.
Anchorage - Flat top is our "social" climb, it's usually an after work hike. Not too long or rigorous, I suggest it for the views. Port Woronzof is pretty cool, it's along the coastal trail and has a nice view of the inlet. Beluga point and McHugh Creek are about 5-10 miles out of Anchorage (depending on where you're coming from) going south on the Seward Highway. Portage Glacier is pretty cool too, it's farther out though, past Girdwood (cool place but nick-named "Girdweed" for well-known reasons). There is also a hostel in Girdwood.
Seward I recommend the cruise, Mt. Marathon is awful around the 4th of July, because of the marathon. Other than that people run it, it's steep but completely do-able.
Valdez is awesome because you're completely surrounded by mountains. Fun place to fish.
Hope this helps!
Melissa