Read the book "Unofficial Guide to Last Vegas". Try to gather up as many coupons as you can ... good site:
http://www.vegas4locals.com/coupons.html
I don't think you need a rental car for the first visit, but be prepared to walk-and-walk-and-walk.
Check out public transportation such as the Duece/Ace buses. Also monorail (costs $$) that run along the backs of some of the hotels. There are also some free trams that will be listed in the above book.
Be aware that all of the MGM properties also charge a "resort fee" which can be as much as $18/day ... take that into account when you are booking a room (read the fine print). We have liked the tower rooms at the Luxor and also like Monte Carlo (MGM properties). We've stayed at Bally's (more centrally located). If you are without a car, I'd recommend staying on the strip (but no further North than TI/Mirage area). Book your room directly from their website and book ones that have good cancellation policies. Then check periodically to see if the rate has come down and/or you find something better. I typically will book, cancel, rebook several times before a trip ... saving lots of $$$.
Try the $20 trick when you check in .... sandwich a $20 between your ID and credit card at registration and kindly ask if there are any complimentary upgrades available. We've usually gotten upgraded (e.g. Luxor from Pyramid to Tower / Bally's from South Tower to North Tower). If they can't accomodate you, they will give the $20 back.
Since it is your first visit, get a couple copies of the American Casino Guide. They have lots of coupons where you can get free slot money when you join a casino's players club. I think we got $25 at the Venetian ... we'd just play through that amount and then "cash out". But we would have lots of fun going from place to place using the coupons. This is a great way to have fun without it costing money (except for the book).
IMPORTANT: Make sure you tip the drink servers at least $1 per drink, whether it is just bottle water or a cocktail. If you don't, they won't come back!! Get your money out at the time you order ... and, yes, they take chips!
Have a great time!
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Just read some of the responses. Yes, we like Monte Carlo. The last time there, I thought the room was a little run down, but we'd just stayed at an MGM suite! Good location, the MC and just a tram ride to the Bellagio! Don't forget the resort fee for MC which is $16.80 per day - due at check-in.
At the airport, take a cab to your hotel ... tell the driver "NO TUNNEL" otherwise, you can get long-hauled (extra money).