Take US 93 southwest of Las Vegas, pass through Boulder City, and head toward Hoover Dam. At the intersection of the US highway and Lakeshore Drive, (NV 166) is the Alan Bible Visitor Center, headquarters for the 1.5-million acre Lake Mead National Recreation Area, largest in the Lower 48 states; it encompasses the 110-mile-long Lake Mead, largest manmade lake in the Western Hemisphere.
Turn left on Lakeshore Drive, which hugs the western shoreline. A mile north of the visitor center on Lakeshore Drive is Boulder Beach, the closest (roughly 30 minutes from the Strip, depending on traffic) and most popular beach to the city. However, bring your flip-flops; it's mostly rock, little sand. Also, with the present low water conditions (down nearly 100 feet from full), Boulder Beach can not only be a bit rough on the feet, but also dangerous. Since today's shoreline used to be hundreds of feet offshore, there's some broken glass from bottles that were thrown overboard from boats moored offshore years ago. The north side of the beach is reportedly safest.
Eight miles north of Boulder Beach is Las Vegas Bay, which has a campground on a bluff over the lake and the marina where you catch the Desert Princess, the 250 passenger Mississippi-style sternwheeler that cruises the lake. Though there's no real beach at Las Vegas Bay, you can take a walk and find a place to get wet.
A mile north of Las Vegas Bay is an intersection with NV 167, also known as Northshore Road. Take a hard right to continue northeast along the shore of the lake. Seven miles from northeast of the intersection is the turnoff for Callville Bay. Again, this marina has an RV park, shady campground, visitors center, convenience store, and houseboat rentals, but no real beach. It's still cool to visit, though, given that it's one of the largest and best inland marinas in the United States.
Still, it's worth it to continue another 25 miles to Echo Bay, the best development on the Nevada side of Lake Mead. Two campgrounds accommodate the few in-the-know RVers and tent campers who make it this far from Las Vegas (a whole hour) to commune with the heat, sweat, and flies of summer; a motel, restaurant, bar, and houseboat rentals take care of the city refugees who are reluctant to rough it. The beach is sandy, shallow, secluded, and has a bit of shade.
Again, note that the lake level has dropped dramatically after eight years of drought in southern Nevada, so the "beaches" might be a little different than they should be. Still, these are the places to get to the water, such as it is.