I just wanted to clear something up for you about vacation home rentals in Las Vegas. The recent ordinance was for the City of Las Vegas, not N. Las Vegas, Clark Co., or Henderson, although the last two do have their own short term rental regulations.
The city doesn't include the area around the Strip, it begins north of Sahara and is sort of L shaped. A map is here...
There is often some confusion about what is Las Vegas the city, and what is Las Vegas - unincorporated Clark Co. Two completely different entities.
Back to the city's ordinance, it was rescinded last month and plans to allow them under certain circumstances. The object was to prevent 'party houses' that disrupted neighborhoods.
I did find one management company that handles short term rentals, but sure there must be others. You may want to contact them for more information.
In addition to the great answers below, I would like to add a small point I have noticed recently with Vacation/ Short Term Rentals. As far as vacation type rentals are concerned I have noticed many of the management companies are seeking homes with pools and they seem to be pretty concerned with location. I would recommend speaking to a management company as provided below. Convenience to the strip seems to be a recurring theme, consider looking into these variables before you buy, it may make it a safer investment for you.
It also lists 3 of the short term property management companies in the article.