Actually, see any of the Spiegelworld shows
If you see any show in Vegas, make it one of Spiegelworld's. The company redefined entertainment on the Strip with Absinthe, which took the familiar Vegas show, turned it on its head, doused it in gasoline-laced absinthe, lit it on fire, and danced naked around the flames. Opium did the same, but did it on a spaceship heading back to Las Vegas from Uranus. Now Spiegelworld has once again ups its own ante with the phenomenal aforementioned Atomic Saloon Show, which somehow manages to be even more batshit crazy and lewd than its predecessors, and coming from someone who has seen the previous shows several times, trust me when I say that is a HIGH bar to clear. If you and your date are at all prudish, these are not the shows for you.
Explore the booming Arts District
Dunno if you're noticed this yet, but DTLV's 18b Arts District has undergone some major transformations lately, with killer bars, restaurants, and breweries now opening at a breakneck pace. The Arts District is the closest thing that Vegas has to the kind of bustling, walkable neighborhoods with lots of foot traffic and street retail that other major cities take for granted. In no particular order, eat and drink at Esther's Kitchen, Jammyland, Able Baker Brewing, AdCraft Kitchen, Cornish Pasty Co., Hop Nuts Brewing, Velveteen Rabbit, CraftHaus Arts District, Three Sheets Craft Beer Bar, Vesta Coffee Roasters, Makers & Finders, 18bin, and Artifice. Peruse "Antique Alley," which is full of kitschy retro antique and vintage stores. Catch a quality independent theater production at the Majestic Repertory Theatre or Cockroach Theatre. And, of course, explore the galleries and artist studios at the Arts Factory and Art Square, check out the public art installations like "Paintbrush Gateway" (don't worry, you'll see it), and don't miss the monthly First Friday arts festival/block party.