The Clark County Heritage Museum, on Boulder Highway. There's several old buildings you can go through, including the P.J. Goumond home, the Beckley home, and a couple of buildings that used to be part of the Last Frontier Village (which was part of the second resort on the strip ).
http://www.nevada-history.org/museumessay.html

Do you go downtown? LaBayou used to be the Northern Club, which received the first gaming license issued in Las Vegas in 1931.

Check out Binion's, there's a nautical looking light fixture (King Neptune I think?) hanging over the bar behind the craps pit...reportedly that fixture came from the gambling ship the SS Rex, which was owned by Tony Cornero. He ran the LV casino for a short time, also known as the SS Rex, and had the light fixture put in.

While you're at Binion's, go up the stairs that are near the newsstand (also near the stairs down to the coffee shop...but closer to the newsstand). The part of the hotel that you're in used to be the Apache Hotel, built in 1931. The Apache had the first elevator in Las Vegas...but I'm not sure if it's still there, or which one it is.

You can also check out the El Cortez. It was originally built in 1941, and you can still identify parts of the original structure. I think it's the oldest continuously operating casino in Las Vegas.

Go out Bonanza Road, you can see what's left of the historical Moulin Rouge. A little further down the street is what's left of Benny Binion's house.

Have fun!!