This is the perfect place to take someone who has never been to Las Vegas. It's a unique experience that can be done for very cheap.
I'd recommend going at sunset for three reasons:
1) The view is fantastic. The sun sets behind the mountains, which gives them a glow as the city begins to light up.
2) 2 for 1 happy hour from 4 to 7 PM. This applies to martinis and appetizers only. Keep in mind that they bring both of your drinks at once, which makes things more fun.
3) The dining room on the 106th floor is bustling at dinner time and, yes, it rotates. Lean over the railing and check out the rotating clientele but be careful, you might experience some vertigo.
A few other things to note:
1) Live jazz!
2) Bungee jumpers will occasionally fly past the window.
3) The elevator that takes you to 107 is incredibly fast. It's not for those with weak stomachs.
4) The Deuce is an easy way to get there. Stratosphere has it's own bus stop.