+1

Paris is a good starting point. I also suggest Venetian, because you can get to Palazzo, Mirage, and Treasure Island.

Some hotels are connected by free trains. For example, you can go between Bellagio-City Center (Aria, Cosmopolitan, Mandarin Oriental), Mandalay Bay-Luxor-Excalibur. Just make sure they run 24 hours. No need to take the pricey monorail that takes you a football field away from where you're going.

If you want to cruise down the strip, there's the double-decker Deuce bus. But I'm not sure what their schedule is. It's about $2 each way.

Have fun. Go win some money.