Get in your car and go about 400-600 miles per day unless there are 2 of you and then go all the way in a day, then go slow on the way home so you can recover for work or school- or whatever.

Bring your bikes, bikes in the park are an easy way to get around.

STARTER MAP http://maps.google.com/maps?f=d&hl=en&saddr=los+angeles,+ca&daddr=Livingston,+MT+59047&ie=UTF8&om=0&ll=43.707594,-111.049805&spn=4.860223,9.887695

Here’s the way to go. Make sure you see Zion, Bryce, Flaming Gorge, in UT on the way.

And once in Yellowstone, go to the “45th” swimming hole. It’s the best place in the park and is near the Mammoth campground, just go down the hill. Walk from the campground, just ask around.

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Heres the NPS description:
45th Parallel Bridge and Boiling River

A sign near where the road crosses the Gardner River marks the 45th parallel of latitude. The 45th parallel is an imaginary line that circles the globe halfway between the equator and the North Pole. This same line passes through Minneapolis-St. Paul, Ottawa, Bordeaux, Venice, Belgrade, and the northern tip of the Japanese islands. It is, here in Yellowstone, roughly aligned with the Montana-Wyoming border.

A parking area on the east side of the road is used by bathers in the “Boiling River.” Bathers must walk upstream about a half mile from the parking area to the place where the footpath reaches the river. This spot is also marked by large clouds of steam, especially in cold weather. Here, a large hot spring, known as Boiling River, enters the Gardner River. The hot and the cold water mix in pools along the river’s edge. Bathers are allowed in the river during daylight hours only. Bathing suits are required, and no alcoholic beverages are allowed. Boiling River is closed in the springtime due to hazardous high water and often does not reopen until mid-summer.

BUT if you sneak down there with your swimtrunks and towel, you can priately go in- barring high water and pesky rangers.