We go to Vegas pretty much every year, with our now-7-year-old. 3 years old is a touch harder, because some of the stuff I'd recommend (arcade at NYNY, and go kart racing at Pole Position Raceway) he/she probably isn't quite ready for yet. But we did take ours when he was 3, so here goes:
Rule 1: bring a GOOD stroller with a nice umbrella, like a lightweight Maclaren. Vegas is a LOT of walking, and it's nice to have a place to throw your stuff so you don't have to carry it.
The most kid-friendly hotels are the Excalibur and Circus Circus. CC is pretty run down, but has the Adventuredome theme park and the trapeze act. Don't even bother trying Wynn/Encore, as (at least the last time I was there), they HATE kids and will try to push you out as quickly as possible, while making you miserable while you're inside.
Couple of fun family-friendly attractions, in no particular order:
Adventuredome at Circus Circus, mentioned above
Ethel M. Chocolate Factory, out in Henderson (15 mins from the strip)
Paradise Gardens at Flamingo
High Roller observation wheel (550 feet high!) at the LINQ
The LINQ in general--there are fountains, live music, lots of restaurants, and the Purple Zebra slushy shop
Car Collection at the Quad--we took my son when he was 3 or 4 and he loved it
Gondola rides at Venetian/Palazzo
Fountains at Bellagio
Volcano and secret gardens at Mirage
Shark Reef at Mandalay Bay
Moving statues in Caesar's are currently closed for renovations, not sure when they're re-opening
Yard margaritas at La Salsa (lots of locations)
Rainstorm in Miracle Mile shops at Planet Hollywood
Kid friendly shows:
Nathan Burton Comedy Magic (Miracle Mile Shops at Planet Hollywood)
Mac King Comedy Magic (Harrah's)
Cirque du Soleil Mystere (Treasure Island)
That's all I can think of at the moment, but if anything else comes to me I'll post it. Feel free to ask any additional questions as well.