I've stayed at the Prospector twice in the past 14 years, once ten years ago and once in 2005. The first stay was not pleasant as the place was old and run down and dirty. It was a whole new hotel in 2005 when we went down to Juneau for Thanksgiving with our daughter. The outside still doesn't look like much, but the interior decor has been completely renovated.
We had a one bedroom suite on the 3rd floor overlooking Gastineau Channel. Well equipped kitchen, comfortable furnishings, a great view, and HS wireless internet connection (one of the first in Juneau). The location is just far enough from the Capitol that it makes for a chilly walk in the winter, but that also means it is away from the cruise crowds in the summer - a major plus.
The attached restaurant/bar, TK Maguire's, serves solid food similar to TGI Fridays. Next door is the Alaska Museum and Centenial Hall - the convention center.
So for downtown Juneau, my first choice is still the Goldbelt. The Prospector and the Baranof are tied for second in my mind. Prospector has nicer rooms, the Baranof has great public areas.
Update (Nov 2010): Tried to reserve a suite here this month and was told that children are no longer welcome. Guess I won't be staying here again, even if we don't have kids with us.
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Address: 375 Whittier St., Juneau, Alaska, 99801-1781, United States