That is exciting!
There is so much you can do and have not have it cost you a lot.
There is:
Bellagio Water Fountains. I think you can get a list of what songs play when off of their site. They also have a Conservatory on the main floor of their casino that they change every season, they do it all in live flowers and plants. They have performances inside their shopping area if I am not mistaken. They have a delicious Sunday Champagne Brunch, about $40 or so, so little high, but the food they offer Yumm!
Mandalay Bay: The House of Blues restaurant is there and I go there every time I visit Vegas. They also have the Shark Reef if you like looking at Ocean animals. I can't remember how much this costs now. Their pool area is Amazing!
Venitian: Shopping (as in all the Casino's!) They have a Canal ride you can do, bit pricey if I remember right, but I took my then 12 year old on it and she got a kick out of it. They also have performances inside their shopping area, it is either the Bellagio or the Venitian that puts on a nice little Opera. Try and catch those, they also have some other little things they do.
New York New York, they have a little Irish Pub there (If I remember the right place) that was good, can't remember pricing on it though.
Treasure Island: They have a show at night (outside) with Sirens of the Sea, good interaction between two different Pirate Ships and songs. Might be a bit Riske, didn't get a chance to see it last time I went.
Mirage: Their Volcano errupts every night. I think they have the Dolphin Encounter as well, but you have to pay for that.
MGM Grand: They have the White Tigers habbitat, great to see and free. It's on the ground floor of the Casino. Rain Forest Cafe is also there.
As you can tell, those are my three favorites. Each Casino offers such a different atmosphere, I would really soak those up it's a great experiance.
As you can tell you will not want for something to do, if anything, Relax and enjoy your first trip without the kiddies!