Best Hotel on the strip for under $200/night

I've been to Vegas more than 30 times and stayed at 15+ different hotels.  Vegas prices fluctuate a lot so depending on the time you're going you might actually be able to stay in the best 5 star hotel Vegas has to offer at that budget.  If there is a big show / convention going on when you're there those same hotels could be double that price.  Without knowing the actual dates I'll start from the best of the best:

1. Wynn Hotel Las Vegas - amazing service and top notch luxury
   
2. Bellagio Hotel - perfect location, great luxury
   
3. The Venetian - also perfect location and huge rooms, every one is a suite
   
4. The Cosmopolitan of Las Vegas - best for younger groups but also tends to be the most expensive
   

If you're not worried about luxury I'd recommend any of the following as "solid choices"

1. MGM Grand Las Vegas - huge hotel that usually has great prices and recently renovated rooms.  Get the double queen rooms if sharing - they're bigger and worth it.  The west wing singles are tiny.
   
2. The Mirage - I really love this place since they renovated.  perfect location right in the center of everything and its smaller so you can get to the strip without walking 20 mins through the casino.
   
3. Treasure Island - great location next to The Mirage but its not quite as nice.  I could hear people in the hallways and rooms but still a solid choice.
   
4. The Hard Rock Hotel & Casino - the only drawback here is the location as its further away from the strip and not easily walkable so you'll be spending more on cabs
   

There are so many great hotels in a concentrated area.  Just stay on Las Vegas Blvd and don't go further south than Mandalay Bay Resort and Casino or further north than Wynn Hotel Las Vegas. 

As for shows I'm not really your guy as I've only seen Love (amazing - saw it 2x) and O (also great but not as much "action")

Feel free to ask any follow up quesitons

Good luck!

Chris' list is a great one.  I'd just like to add two places a bit off the strip. First is Palms Place Hotel and Spa.  It's next to Palms Casino Resort with some super views of the strip from most rooms (ask) and always priced just under strip prices.  It's a very happening place for younger visitors.  There are shuttles to the strip from there I think.  

Rio All-Suite Hotel & Casino is also just off the strip, and is sometimes a terrific bargain.  Enjoy!