Let me guide you
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I live in Las Vegas.
First, if you like Freebies, the MGM has a glass lions den where you can go and see the lions. The fire on water in front of the Mirage is spectacular, the Sirens of TI show in front of the Treasure Island, and the Water Fountain Dance in front of the Bellagio. The mirage also has a place where you can go see Dolphins (not free).
Second, New York New York has a "Midway" where you go to play games such as ring toss, horse race (throw balls into the hole to move your horse), skee-ball, etc. Each game is basically 1 dollar or so, and if you win, you win a toy plushie.
The Circus Circus also has the same thing (better in my opinion). They also have an Adventuredome where you can ride Roller Coasters, Ferris Wheels, etc. You can also go bungee jumping. There are also Circus acts for you to enjoy.
The Stratosphere has the rides and shops on the top
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You can see a birds-eye view of Vegas.
Caesars Palace, you can watch free shows in the Forum Shops (shops like Gucci, Versace, Guess, Prada, FAO Schwartz, etc). It also has a BIG fishtank.
Mandalay Bay has a Shark Reef where you can go underground and walk around as sharks swim above and below you.
You can go to the Luxor and see the ancient egyptian artifacts.
The Flamingo-Hilton has a outdoor zoo type thing where you can go and see turtles, birds, penguins, and fish in their natural habitat. (Free)
The RIO (not on the strip) has a "Masquerade in the Sky" - The best free show in Vegas. They throw beads down on you too.
The Paris Hilton is modeled just like Paris, with big fountains, the Eiffel Tower, and inside, there are shops and tasty bakeries.
The Aladdin has a Desert Passage shopping mall.
.....I think im missing alot of places and I will edit as soon as I remember them
Have a safe and fun trip!! I am positive that you will like it.