The closest In-N-Out Burger is not only close, but actually on the Strip. A branch of the famous southern California fast-food burger chain opened in the LINQ promenade in early 2017.
Otherwise, the three closest are as follows:
4888 Dean Martin Dr..: This location, the closest to the south Strip, is just across I-15 from New York-New York. To get there, take Tropicana west over the freeway; In-N-Out will be to your right, on the corner of Trop and Dean Martin. This restaurant also has a company store, open 10 am-6 pm daily, offering shirts, caps, jackets, and other In-N-Out collectibles.
4705 S. Maryland Pkwy.: This location is about two miles east of the MGM Grand on the eastern edge of the UNLV campus. Take Tropicana east to Maryland Parkway, then turn left.
2900 W. Sahara Ave.: The third location is about a mile west of the north Strip on Sahara Avenue. It's a straight shot from the Strip past I-15, Rancho, and Teddy Drive. If you hit Richfield, you've gone too far.