One of my favorite things to do while traveling solo is to spend a day at the spa. Las Vegas has some of the best spas in the world; steam rooms scented with eucalyptus, reclaimed wood saunas, deluge showers, hot and cold plunge pools all in beautiful and lavish (if not over the top) surroundings. I would suggest either the Encore Spa or Aria Spa + Salon for spa newbies.
If you are getting a treatment (massage, body wrap, etc), entrance into the spa is included. I suggest spending at least a couple of hours before and/or after your treatment enjoying the amenities. If you don’t want to pamper yourself (read: splurge) on a treatment, some spas offer day passes for a nominal fee to use the facilities.
One thing I think everyone should know before going to the spa: it is best experienced naked. Large spas are divided by gender. Yet, time and time again, there are always a few guests wearing bathing suits. I consulted with a female friend of mine and she said the same thing happens on the female side.