You can stay in Carson City itself, or Reno is only a 30 minute drive while South Lake Tahoe and Incline Village at the Lake are a 60 minute drive. There are hundreds of hotels/motels in the area that can provide you the experience you want.
However, if you want to stay in Carson City, the cheapest and closest to the Carson airport is the Days Inn Carson only 2.1 miles away.
3103 North Carson St., Carson City, NV 89706 (775) 883-3343
For more upscale close by the Carson airport is the Hilton – Hampton Inn Suites is only 2.0 miles away and is very nice.
10 Hospitality Way, Carson City, NV, US 89706 (775) 885-8800
Trip Advisor is always a good resource for more detailed research on hotels in Carson City, or any where else you want to stay.