During the week I stayed at the Mirage and that was a dream. At the weekends I found a couple of dives: one was a Travelodge and the other was a greasy-spoony sort of raggèd hotel just south of the Strip, over the Interstate highway bridge, where I distinctly remember some crazy guy screaming and kicking walls and bins around one morning while I was gobbling my brekkie! (He didn't seem to be armed, however.) Even those near-Strip/off-Strip dives were overpriced 'cause it's expensive at weekends when all the raff come up from LA to play.
I can second the Travelodge on the strip. It's like the best kept secret on the strip, IMHO. Real dive, but if all your doing is sleeping there, it's one of the best locations, everything is pretty much just a walk away. Nowadays though I could probably afford something a bit nicer, but as someone fresh out of college and going on it cheap, it was great.
Also, Mandelay Bay has pools and often has a few good deals. Plus it's right next to the airport, so when you show up, the taxi or bus ride is dirt cheap comparatively. Also its an equally-quick jaunt to get back to the airport, which can be really helpful if you have some weird departure times and are worried about time. A negative is that it's at one end of the strip, so you're going to be paying the bus fare pretty much every day if you're not up for a lot of walking.
I've seen Cirque du Soleil and Penn & Teller. Being a libertarian, I obviously enjoyed the latter more, but the Cirque show I saw was pretty cool, I'm not going to lie. I am not sure it was worth what I paid, but if you are going with a date, it's going to be your best/safest option. If you're just going to have fun and an enjoyable time, go see Penn & Teller instead and hang out a bit to watch the dancers at the Rio and maybe play some Roulette while you wait.
Also, don't forget to hit a few of the rides at the Stratosphere. Make sure you share your brainwallet info with a loved one before you get on the rides though.
