I used to do it in Vegas all the time. There's a couple of rules you should follow, and you'll be fine.
1. Make sure you *look* 21+. (If you look 16, don't even bother)
2. Carry a drink in your hand at all times. I can't stress this rule enough. If you act like you're not doing anything wrong, no one will think any different. They see you carrying a drink, they assume you got carded somewhere, and it's not their problem anymore. Vegas does not have an open container law, so you can walk into the casino off the street w/ a drink in hand. (It's helps to be carrying the same type of glass/container the drink girls will be serving you inside)
3. Start small. Hit up the slot machines, get aquainted w/ the drink girls. These girls can be used to your advantage. Remember to tip well.
4. Move to an area within your drink girl's zone, but also within view of the tables and/or bar. Whether they are aware of it or not, the dealers/bartenders will notice you.
5. Finally, when you feel comfortable, move to one of those tables or to the bar. (If you feel comfortable enough, I'd recommend the bar. A bartender can be an extremely valuable asset. No one is going to give you crap if the bartender recognizes you.
Remember, if anyone ever questions you, freak out like you must've *lost* your wallet, and tell them that you need to get back to *your* hotel asap to report it missing.
Best of luck!
evans