The Reno area has made a name for itself as one of the only places in the U.S. where you can get All-You-Can-Eat sushi for around $25 per person...and it's excellent. Sushi bars and restaurants have popped up all over the city and you can pick and choose whether you want your sushi in a traditional way at Sushi One or deconstructed and DIY at FinBomb Sushi Burrito & Poke Bar.
If you like to experience different flavor combinations from other countries, try the Taiwanese Burgers at 101 Taiwanese Cuisine in Downtown Reno or the pho at Golden Flower the the shadow of the Reno casinos. If you are on the lookout for Dim Sum, Caie's Oriental has a huge selection of wonderful Chinese tidbits to taste. And, of course, don't forget some of the best Thai food in town at Thai Lotus.
Speaking of the Reno casinos, they also have an excellent selection of Asian cuisine including classic Chinese food at Chi at the Peppermill and both sushi and teppanyaki at Ichiban at Harrah's.