I had quite nice experiences at the Hilton. Stayed there three times (different days) on a trip. Also stayed at the Hampton Inn in Anchorage (which was surprisingly nice for an HI).
The Hilton is quite conveniently located to many things (mall and many restaurants/shops are easily walkable).
I can't say how the Sheraton compares as I've never stayed there, but it doesn't seem to be quite as conveniently located.
The Captain Cook is, IMO, overrated. I stayed there once and paid an arm and a leg in March for a basic room. Free Internet access was nice, but not worth the price of the room.
Guess I'll have to check out the Sheraton now...
