Some good answers so far, so I will just add what I can.
Free stuff to do
Fountains of Bellagio
Blown-Glass Sculptures - Bellagio
Sunset Stampede - Sam's Town
Sirens of TI - Treasure Island
Volcano - White Tigers - Mirage
Penguin Habitat - Flamingo
Atlantis & Festival fountains - Caesars Palace
Statue of Liberty - Brooklyn Bridge - NY NY
Eiffel Tower - Paris
Lion Habitat - MGM
Ethel M Chocolate factory & Botanical Gardens
Antigues & Artifacts - Main Street Station
Sports Memorabilia - Vegas Club
Gold Nugget collection - Golden Nugget
M & M World
Circus acts - Circus Circus
Auto Collection - Imperial Palace(with coupon)
Masquerade show in the Sky - Rio
Carnaval Court - Harrah's
Merlin vs Dragon - Excalibur
Shopping
Forum Shops at Caesars Palace
Dessert Passage - Aladdin
Grand Canal Shoppes - Venetian
The Fashion Show Mall
Rides
Deuce(strip bus)
Monorail
Insanity - Big Shot - X Scream - Stratosphere
Manhattan Express - NY NY
Star Trek - LV Hilton
Speed - Sahara
Adventure Dome - Circus Circus
Top of the Eiffel Tower
Gondola's - Venetian
AJ Hackett Bungee jumping
Flyaway Indoor Skydiving
Fun stuff for a few $$
Shark Reef - Mandalay Bay
Madame Tussauds
Siegfried & Roy's Secret Garden & Dolphin Habitat
Have photo taken with one of the Lion Cubs at MGM
this is the best site I know of for up to date LV info
http://www.lasvegasadvisor.com >all the buffets with times, prices & ratings>shows, nightclubs, restaurants, etc>all with info and links to their web sites>
My favorite buffets for great food and good value
Main Street Station
Boulder Station
Orleans
Fremont >Tue/Fri/Sun Seafood buffet
Romantic restaurant(expensive)
Michael's - Barbary Coast
Romantic restaurant(moderate)
Top of the World - Stratosphere >rotates 360 degrees once per hour
Steakhouses(moderate)
#1-Pullman Grille - Main Street Station
#2-The Range - Harrah's
#3-Prime Rib Loft - Orleans
#4- Billy Bob's - Sam's Town
#5- The Steakhouse - Circus Circus
Shows
Mystere - Treasure Island
"O" - Bellagio
"KA" - MGM
American Superstars is a fun show
If you want to see an "old Vegas" style show>The Folies at the Tropicana and Jubilee at Bally's are both very good. IMHO Jubilee is the better of the two.
best afternoon show
Mac King - Harrah's>they hand out 2-4-1 coupons at the booth in the carnaval court next to Harrah's
IMHO - Larry G Jones - "the man of 1002 voices" - at Fitzgerald's is just as good as Danny Gans at a fraction of the cost>
Dirk Arthur "Extreme Magic" - Tropicana is another good afternoon show, tickets are only $29 and there are often 2-4-1 coupons in the "Today in Las Vegas" magazine in your room or hotel gift shop(free)
If you're a sports nut, a great place is the LV Hilton's Super book, you can play video poker(9/6 JOB>99.54? watch sports & drink free.
Play $1 blackjack at Slots-A-Fun - Ellis Island has $1 BJ on weekdays - You can play craps for $1 in a very nice casino, on weekdays the Westin Casuarina has happy hour from 5-10pm, during HH you can play for $1. If you like Pai Gow Poker the Orleans has more $5 tables than anyone.
If you gamble, sign up for and use the slot club card. One of the most fun things about a Las Vegas vacation is opening the mailbox a few months later, finding free and or discount room offers to your favorite hotel.
We go to LV for 2 weeks or more at a time, 2-3 times a year and have for over 20 years. I only recommend things we have done before, some of them many-many times.