Update 2023: I moved to Las Vegas now.
Drive high-end cars on the track
There are several great venues to drive supercars and sports cars in their natural habitat, on the track. By track I mean a proper road course and you drive them at speed. While there are also places to rent them and drive on the street, this would be a frustration for me as you would be stuck in traffic and not get to experience even a fraction of what these cars can do. I wrote a blog article here: http://ltrpca.blogspot.com/2019/03/next-time-you-are-in-las-vegas.html describing some of the main experiences at the track. I also went to Speed Vegas and drove the Ferrari 488, and Exotics Racing and drove a Porsche GT3 RS. Update 2020: Exotics Racing now bought Speed Vegas and merged to the Speed Vegas facility south of town. Another venue is Dream Racing where I drove a C8 Corvette in 2023.
There are others. You can drive off-road or NASCAR experiences too. The Las Vegas Motorplex is a center of much of this. This is my favorite car thing to do in Las Vegas by far, but it is also the most expensive. Plan to spend a few hundred dollars but it is well worth it. Many exotic cars are ridiculously expensive to buy and own. Once you spend that much, most people don't want to risk that investment by taking them to the track and driving them hard. Here you are just renting the car (insurance included) so no worries. You can really have fun in them and give them back when you are done. You get an experienced instructor to show you the line and how to get the most out of these cars at their track. It's the best way to experience these cars.
Note: in 2020 Exotics Racing bought Speed Vegas and merged these operations to the Speed Vegas track.
Drive your own sports car on the track
Spring Mountain Motorsports is just around the mountains near Pahrump (less than an hour away). It features many tracks, my favorite being Charleston Peak (shown below).
Driving here requires that you find an HPDE, register well in advance, and have your car inspected and prepped for the event. Find and register for most events either at MotorsportsReg or Club Registration. Caution: this is very addictive!
Drive Go-Karts
There are many places too drive go-karts as well, both indoors and outside. Exotics Racing offers both supercars (above) and go-karts. I have driven the electric indoor go-karts at Pole Position which is close to the strip. It's inexpensive and fun and since it's indoors and the karts are electric you don't have to deal with the weather. There are many others.
Visit a museum
Here is a great article highlighting some of the car museums. I have been to the Shelby facility, both at the old location near the speedway, and the new location South of the strip.Shop for car related stuff
Being a Porsche fan I found a rare Porsche Design outlet shop. I think there are only 2 of these in the country, one being at the Las Vegas Premium Outlets mall North of the strip. Porsche Design merchandise is not cheap so finding it at a discount is great. Of course the Shelby store is a great place to shop and every Saturday morning they have a cars & coffee.
Go for a road trip
While Las Vegas is in a desert, it is close to mountains and lakes too.
Hoover Dam and the Mike O'Callaghan–Pat Tillman Memorial Bridge
View from the Mike O'Callaghan–Pat Tillman Memorial Bridge
It's a short drive (about 40 minutes) from Las Vegas to Hoover Dam. There is also a great view from the bridge to the South of the dam. You can walk across the bridge.
Biking on the Lake Mead Historic Railway Trail
Mount Charleston
Mount Charleston is a short drive (about an hour) from Las Vegas where you can get away from the desert and enjoy the mountains and pine trees. In the winter it is often snow covered. In the summer it is much cooler than Las Vegas, often by 30F. My Charleston can be very crowded at times. You can see the traffic and congestion in the video below taken the day after Christmas.
Mt Charleston the day after Christmas 2022
Mountain biking on Mt Charleston in the summer
Valley Of Fire
I have actually not visited this yet but I plan to soon and I will update then.
Red Rock Canyon
Red Rock Canyon is the most visited park in the country with over 2.5M visitors each year. There is a scenic drive and many hiking trails but you must get a reservation to enter.
On the way to Red Rock Canyon there is also Calico Basin which is very colorful and has several trails as well.
Zion National Park
Zion National Park is less than 3 hours away. There are great hiking trails and camping as well as hotels and lodges.
Mountain Biking
The Las Vegas area has many mountain bike trails. I use Trailforks to find most of them: https://www.trailforks.com/region/las-vegas/?activitytype=1&z=9.2&lat=36.19202&lon=-115.28210 . In the winter the lower elevations are great. When it gets hot in the summer, go to higher elevations like Mt Charleston. Some bike shops offer bike rentals, including some offering electric mountain bike rentals. Las Vegas is also a bike friendly community with many paved road biking paths.