Terry Gilliam's adaptation of Hunter S. Thompson's Fear and Loathing in Las Vegas is a fascinating look at the end of the counterculture hippie movement, Gonzo journalism, and even at Las Vegas itself. The main characters, Raoul Duke and Dr. Gonzo definitely put the "sin" in Sin City, and the Gonzo journalist thing to do would be to experience Vegas's distinct culture for yourself. Whether or not you take a page from Duke and Gonzo's book and pack a sh*tload of hallucinogens to sample while exploring the city...well, that's entirely up to you.
Red Rock Canyon was the perfect place to film some of those desert driving scenes.
Jean Dry Lake was where the off-road race, the Mint 400 (which Duke was supposed to be covering) was filmed.
The event was briefly brought back after a few years of not being held at the Moapa Paiute Travel Plaza / Sinclair Gas around 2010.
Also check out the Pioneer Saloon, where the hardware barn scene was shot, and be sure to visit Baker...it's a great place to sober up and sleep off your delirium.
Back in Vegas, you could hit the Las Vegas Strip to holler at out-of-towners...
But I'd suggest a visit to the Neon Boneyard at the Neon Museum, where you can see the vintage signs that lined the main drag back when Hunter S. Thompson rolled through. The movie's Director of Photography was partially inspired by the Boneyard when recreating the 1970's feel of the film... and bonus! They have the Stardust Hotel sign and the Binion's Horseshoe sign that would have been up back then.
The casino that inspired Bazooko Casino, Circus Circus Hotel & Casino, actually didn't want to be associated with the film, so the now-closed Boardwalk Casino stood in. The film crew even recreated the carousel bar (which rotates in the opposite direction of Circus Circus's Horse-a-Round bar to deflect suspicion).
They also stay at (and trash) The Flamingo and Stardust Hotel (yet again, no longer open).
And if you visit, you'll find that more than just the signs have changed. Desert Inn is now the Wynn Las Vegas and the Mint Hotel is now Binion’s Horseshoe, and (ironically enough) the Dunes, where the National District Attorney's Convention happens, is now the Bellagio.