How much time will you have? Seems like every time I go I never make it through my list of things to do.
Eat at the Red Square. It's a Russian resturant on the ground floor of Mandalay Bay. The food is pricey, but very worth it.
Definately spend an afternoon walking through the forums at Caesar's Palace. Set a limit on what you have to spend though. While you're there, look for the mexican bar that serves the 3ft. margaritas.
Have breakfast at the Paris. The crepes are great.
Hit the Fontana Bar in the Bellagio for an evening show. If the house band that night happens to be a group called Isis, tell the singer (Kevin) that Adam says hi.
Roller coaster at the New York New York is a lot of fun.
Hofbräuhaus is mandatory. An exact replica of the one in Munich where Oktoberfest started. The food is authentic German, and so is the beer. The beer is served in either half- or one litre mugs. Personally I'm a fan of dark (dunkel) but they're all good.
Blue Man Group is a great show. I'm told Cirque du Soleil is great too, but haven't caught one yet. Everywhere you go you'll be constantly surrounded by ads for shows playing, it should be easy to find something you'll enjoy.
Carry small bills for tipping. It's pretty much customary (but not required) to tip everyone who does something for you (especially at the bars, resturants, and in the cabs). Just don't do it on the casino floors unless you're familiar with the proper way to do so. And don't carry enough cash to make it worth getting robbed. All the hotels have safes in the rooms for your valuables.
Wear comfortable shoes. You'll be walking a lot. How you dress is up to you, but some places do have a dress code. Clean jeans, a nice shirt, and a suit jacket will be fine for pretty much anywhere.