The forward approach will work well in this situation. This is where you call the casinos and ask them what they will offer you to come to their casino to do some gambling. In most cases the casinos may offer you some free meals and maybe even a show. If you call and tell them you are bringing a group of people to their casinos they may even go as far as to give you a suite for yourself and give a break on the other rooms for your trip.
A variation of the forward approach is to call a casino and get them to give you a comp then call all the other casinos and see if they will match or beat the other casinos offer. If you can convince them you are worth them bringing you to their casino they may just try to outbid the previous casino, and if they really want you they may pick you up from your home or the airport depending on where you live in a limo and convince them you are a high roller in the casinos and they will send a private jet for you, but that is usually reserved for people who have won at least $50,000 from that casino or more.
If you just show up at a casino to play the table games it is also simple to get them to give you a free room for the night, especially if you are winning. If you come to the casino and win some of their money they will most likely just offer you a room for the night. They do this in the hopes you will continue to play and not only lose your winnings but all the money you brought with you as well.
You can get comps without ever spending a dime in the casino, but you have to have a few grand with you at the time you arrive at the casino. Bring a briefcase with $10,000 in cash in it. Before you get to the casino call them and ask them if they can place your cash in their vault for safe keeping. Chances are good they will offer you a free room and some other comps when you arrive so that you can spend all your money in the casino. as a matter of fact most casinos will not ask to verify the money, so you can just bring in the case and they will assume its full of money and think you are what the casinos refer to as a "whale" this term means high roller, or someone who drops lots of cash in the casinos.
When ever talking to the casinos you need to give off the vibes that you are wealthy and will drop some serious cash if the casinos make it worth it to you. This is not easy to do but with some time and practice you will be able to walk into any casino and they will lavish the freebies on you.