There's a bus from the airport into town/strip. On the way back to pick up a car i had to sit next to some rather large rather smelly lady though. Can't remember cost, was cheap. Also involved some J walking across 6 lanes.
Grand Canyon, south is very commercialised i'm led to believe, so i went north side. Took a hike for maybe 10miles then back due to time restrictions. But that was enough to lose all the people and see some cool birds and things.
I rented a car from the airport however.
Getting a walk in i'd recommend if at all possible, viewing platforms are cool and all, but you know..
There's Valley of Fire state park right next to Vegas, so not going there is dumb if you have a car imo.
Zion national park was my favourite out of all the local parks, search Angels Landing. It's pretty scary when you think about it, but it's very awesome and worth it. Among other amazingly cool stuff. Standing from a viewing platform looking at a whole, versus being alone on a cliff face walking into tight caverns where the majority don't go...
Oh, and there's Coral Pink Sand Dunes also. Fun if you like sand.
Though if not into all that nature hiking or scrambling stuff, a plane flyover would be very cool. See if you can get to Canyonlands fly over also.
There's a party like hostel just off the strip. Maybe 3 mile walk away. Dirt cheap, and everyone there is merely there to party. Area is a bit iffy, but inside the hostel complex is fine. -if you can perhaps stay in US for longer.
Don't ever recall seeing a monorail. But i went on one of the funky rides at the top of one of the towers. That was fun and scary. Worth a punt.
Can't recommend any buffet places. But, if you can get on a travellers forum and ask around you should hopefully get some insider knowledge. One local guy picked me and took me to out of town place, i seem to recall him mentioning it was the best in Vegas, but sadly can't help you there besides the forum thing. I do remember him being funny about me paying my way, and they had broccoli available. -It was breakfast time.