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Dawson City ... you either get it, or you don't. It's not a fancy place ... gravel streets, wood boardwalks, old buildings, and tourists. The old buildings are interesting. And so are the outlying areas.
It is worth making the trip to the top of Dome Mountain and driving the road out to the national historical site at Discovery Claim (although not as interesting now as it was 10 years ago). Visit Bear Creek and whatever else strikes your fancy. The Visitor Centre in Dawson City is a great resource.
We have camped twice at the Yukon gov't campground on the Klondike River, which is a ways out of town, and twice at the Yukon gov't campground across the Yukon River, both with no services. We have also camped twice at a commercial campground that is a couple miles outside of downtown and it was okay. The RV park that is in downtown Dawson is convenient to downtown but has VERY tight quarters. Your choice ...
Our visit in 1993 was very interesting. In 2008, the historical sites (Discovery Claim, Bear Creek) were not as interesting. Not because we had been there before, but because the sites were not as well-maintained and not staffed with interesting folk dressed in period costume who could tell explain the history of that area.
In 2008, we had planned to spend a couple of days visiting the area. However, we were there for only an afternoon and evening.
Many of the historical sites are outside of town; to truly see the area, you must explore with a vehicle. If you can't drive around, I suggest the Parks Canada booklet: South Dawson City Walking Tour (pdf)
These are pictures of the sights ...

Palace Grand Theatre - September 1993 and again
in June 2008

Interior of the Palace Grand Theatre in 2008
Opened in July 1899.
http://www.pc.gc.ca/lhn-nhs/yt/dawson/natcul/natcul2_e.asp

Government House - September 1986
http://www.pc.gc.ca/lhn-nhs/yt/dawson/natcul/natcul1_e.asp

Red Feather Saloon - September 1986

A rebuilt Red Feather Saloon - June 2008

Strait's Auction House - September 1986
Constructed in 1901 it became known as the Guns and Ammunition Shop.

Strait's Auction House - June 2008

3rd Avenue Complex - June 2008
These buildings are being left as is to demonstrate the effects of permafrost
thawing/freezing.

S.S. Keno Paddle Wheeler - June 2008

Klondike Motors - June 2008

Klondike Thawing Machine Co. building - June 2008

Westminster Hotel - June 2008

Midnight Sun Hotel - June 2008

Lowe's Mortuary - June 2008

Diamond Tooth Gerties - September 1986
Local gambling hall -
http://www.dawsoncity.org/klondikeattractions/diamondtoothgerties/

St Andrews Church - June 2008

Jack London Cabin - June 2008

Robert
Service Cabin - June 2008

Robert Service Cabin - September 1993
Dome Mountain is a must see. On my first return visit as an adult I was somewhat confused about the route up the hill, but after asking at the Visitor's Centre we found the way. Turned out my memory was not wrong; the route that had changed.
A little personal trivia ... when I was a kid, my family visited the Dome for the longest day of the year. The Dome is a popular spot on this special night and there was a good gathering of people up there. Us kids got bored (just what is so exciting about a sun that never sets?), so asked our parents if we could walk back to Dawson City. After getting permission, we started hiking down the road. We were maybe half way when we saw RCMP cruisers heading up the hill ... I didn't learn until later that those cops were responding to a complaint about the party on the Dome. And my mom was arrested for drinking in public!

Ma bear with two cubs beside road to Dome Summit - September 1993

View from Dome Summit looking north on the Yukon River - September 1993

View from Dome Summit looking north along the Yukon River - June 2008

View of Dawson City from Dome Summit - June 2008
That is the "Top of the World" highway on the ridge above the Yukon River.

Standing beside one of the big paddlewheels - September 1993

Sad to see a ship completely collapsed - September 1993

And another about to collapse completely - September 1993
One of two dozen dredges that worked this area, Dredge No. 4 rests on
Claim 17 Below Discovery on Bonanza Creek near the spot where it ceased
operations in 1959. Dredge No. 4 is the largest wooden hull, bucket line
dredge in North America.
More info:
http://www.pc.gc.ca/lhn-nhs/yt/dn4/index_E.asp

Dredge No. 4 - September 1993

Dredge No. 4 - September 1993

Dredge No. 4 - June 2008

Dredge No. 4, Dawson City - June 2008
Bear Creek was an industrial complex of some 65 buildings and related
structures located 10 kilometres (6 miles) east of Dawson City. From 1905 to 1966, Bear
Creek was the Klondike headquarters for corporate mining interests, acting
as the administrative and repair centre for the goldfield's dredging operations.
More info:
http://www.pc.gc.ca/lhn-nhs/yt/dn4/natcul/natcul2_E.asp
We were disappointed that this historical site was closed when we visited in 2008.

September 1993

Ford tanker truck used as a fire engine at Bear Creek - September
1993

Yukon River ferry crossing - September 1993

At the small community of Moosehide, on the Yukon River, looking towards Dawson City - September 1993
Visiting the historic cemeteries in Dawson City is an interesting experience. One can't help but wonder about the lives these people lived so many years ago. I was impressed with the Royal North West Mounted Police cemetery ... there seemed to be so many who died so young ...
Refer to the Yukon government booklet: A Walking Tour of Dawson City Cemeteries (pdf)

Police Cemetery near Dawson City - September 1993

Police Cemetery near Dawson City - September 1993