I've been to Vegas multiple times and there are several do's and dont's. If you're under 21, and attempt to gamble, you may be dissapointed. They are very polite, but pretty firm about underage gambling. My son turned 21 last year and was carded at all the casinos we went in. Don't worry, there are plenty of things to do.
See at least one Cirque de Soleil show. My favorite is the Beatles Love Show. The beauty of those shows is that you will get a great perspective, regardless of the location of your seat. Try and get one show at the discount outlet near the Coca-Cola store or one further North on the strip. We got tickets to Ka at the MGM Grand for $35 each. If you go to the MGM, go to CBS Televison City. We got to be pasrt of a focus group, previewing one of next year's new shows. The 3 shows you mention are all excellent and fun for everybody.
Where are you staying? If your at one of the M-Life hotels, (MGM Grand, Monte Carlo, Bellagio and a few others) they can get reduced prices on show tickets. Bottom line is: shop around for show tickets. Some shows are never discounted: O at the Bellagio routinely sells out and it's difficult to get cheap tickets to that one.
I like your idea of getting out of town for a day. If you know where you're going, renting a car can be good. Do keep in mind that renting a car if you're under 21 might be a bit of a challenge. Lake Mead is great and hiking at Red Rocks can be fun, provided you don't go out in the afternoon in the heat of day. The Hoover Dam tours are good. We went with an outfit called Pink Jeep Tours and they took great care of us, ensuring we had water and access to food during our tour. They took relatively small groups (8) and we found the experience to be really great. Take your camera. The view from the new bridge is incredible.
As noted above, the Fremont Experience is fun. The first time we went was on the anniversary of the moon landing and they had 60's tribute bands playing around that area. Lots of fun and it was free. On the way to that or on the way back, you could go the Premium Outlet center to do some shopping. Lots of good deals on clothes, sunglasses, shoes etc.
On the strip, there will be men and women trying to give you cards with pictures of young women with phone numbers. They can be persistent, but do not take the cards. I watched a guy take a card just to get rid of them and the rest followed him down the strip, harranging him all the way.
Getting around the strip can be challenging. Lots of people feel they can walk, which is what we started to do the first time we went. The distances are greater than you think and the heat can make it tough. We get a bus pass on a weekly rate which allows you to go up and down the strip relatively cheaply. The buses are the Ace and the Deuce. One stops a lot and the other is more of an express, with fewer stops. They can get crowded, but remember, you're on vacation. If you're going to a show, don't wait until the last minute to get there. There are a lot of people on the strip.
In terms of eating, the restaurant business is very competitve and there are coupons, discounts and deals to be had. The buffet at the Rio is good, but it's slightly off the strip and you have to change buses to get there. One of the better deals I encountered was a resturant in New York, New York called America. Food and service were both excellent and the price was decent. We went to an Italian resturant in the Paris Hotel which my wife loved. Your hotel may have some enticements if you eat there and chances are, the experience will be good.
Regardless of your hotel, they want the over 21's in your family in the casinos in the evening. At 8:00pm, they close the pools and every one is out. Take a walk near the Bellagio and see the fountains. Occasionally, street musicians will be impressive. I emphasize occasionally.
Go into the bigger hotels and just wander around. The MGM Grand is (according to my info) the biggest hotel in the world and the 4 largest are in Vegas. Go take a look at the Luxor, the Venetian and go through the Mall at Caesar's Palace. If you have lots of money, you can shop there. If you need a $500 umbrella, they've got what you need.
Bottom line in Vegas is that it's supposed to be fun. It really is an adult playground, but there's plenty to do. The last trip, we stay ed the Monte Carlo and I floated around the Lazy River on my tube with a drink in my hand. Just remember to pace yourself and you won't be disappointed.
