You more likely to get an answer from one of the Las Vegas readers who respond frequently to questions about the area if you give the name and location of the off-strip hotel you are using. There's no way to know which bike shop is reasonably close without that information. I rarely use the LBSs in my area so I have no information to offer you. You can get a list of stores on your own from this site:
Las Vegas Cycling Resources / Directory of Las Vegas Cycling Businesses | Biking YOUR CITY | Biking Las Vegas Cycling You can try calling or emailing stores by zip code for the closest one.