I go to Vegas alone sometimes. It's always a great time. I have a friend who lives there and her and I go out. I've crossed paths with random old friends as well which is spontaneous fun...ala Facebook.
I like solo trips, but I highly recommend planning trips with friends because the memories you get from a Vegas weekend are funny years down the road.
For first time to Vegas, the Strip is overwhelming. It's giant. Some of these properties are remarkable and they just keep opening. Just seeing the Strip could take a full day and night. I think that would be more fun with friends than alone.
If you like to gamble, that's a bonus. I have a great time just playing blackjack all afternoon and making random connections at the tables. You meet people from everywhere.
Food options aplenty. Love eating in Vegas.
Shows, if I were to recommend 3 (though there are many more to see) - 'La Reve' is spectacular. 'Jersey Boys' was surprisingly great. I knew nothing about it and I want to see it again. And of course, you must see a Cirque show ('La Reve' is similar, but not a Cirque show). If you're into acrobatics, I'd see 'Mystere'. I used to like 'O' a lot, but overall show I think 'Mysere'. See 'Love' if you like the Beatles. See 'Zumanity' if you want to be more cabaret. Check out who's in town for concerts/shows when you go. I saw Tiesto at Hard Rock and it was so much fun.
Gay club Krave. I've been once. I had an absolute blast, but I was with my friend and we made great friends with one of the bartenders. Very memorable night, just a ton of fun.
Also, some of the resort spas are incredible. Always spoil yourself for at least one 90 minute massage. They have workout facilities, so you can keep your routine.
Shopping. Everything is $$$, but there are some great stores there, if even only to check out.
I was there last month and stayed at THEhotel. Loved it. Going back in October - and about 10 of my friends are on notice. I hope they go, but if I'm alone...still will be a great time.