Maybe you should start by checking to see what kinds of inputs the club's tv's are equipped with. Usually you will find cable tv inputs, but you also may see rca (yellow composite) jacks and/or s-video inputs. I would suggest that if all of the sets have rca inputs you may want to use those inputs for karaoke video. The reason is that this will not interfere with the house satellite or cablevision systems. The rca wires will connect to a splitter that will lead back to your player/computer video output. By connecting to rca video inputs you will only have to change the television channel to aux when it is time to start the show. Of course, it you should change it back at the end of the show.
If the sets don't have rca input jacks, you may have to run coax cable to the sets. To simplify your set ups you may want to install an a/b switch on the cable input on each set. Then connect the house tv cable to the a side and your karaoke coax cable to the b side of the switch. This will allow you to select your karaoke video by flipping the switches. The other end of the coax cable will be connected to a splitter that leads back to a rf modulator which will lead back to your player/computer video output.
Regardless of whether you need to use rca wires or coax cable, since you wish to run more than one karaoke set, you will need to connect the wires to one or more splitters to divide the video output from your player/computer to the various wires to the various sets.
Your goal will be to use the least total footage of video wires. The more wire you use and the more splitters and/or switches you use, the weaker your signal will be at the sets.
If you have more than ninety feet of video wires or more than two splitters, you will probably want a video amplifier to boost the signal to all the sets. If you are using coaxial cable the amplifier should be installed between the rf modulator and the first cable splitter. If you are using rca cables, you will install the video amplifier between the video output on your player/computer and the first splitter.
The easiest place to buy compatable wires,splitters, a/b switches, rf modulators and video amplifiers is probably your local Radio Shack store.
If you are going to play at the location every week, you may want to set up the wiring once for regular use. Then just disconnect the wire going to the first splitter, leaving the rest of the wires connected for later use. This reduces your setup and breakdown time.
If you have not set up video before, it may take a couple of hours to connect all the pieces and wires the first time including pre show testing. This is in addition to the rest of your set up time. So, take the pressure off of yourself by starting extra early.
I didn't address the s-vido inputs on the back of the sets because s-video wires and adapters are more expensive and complicated to network. However, if you are using a computer output that is s-video you will need a little s-video to rca converter.
I hope that these thoughts are helpful and aren't to confusing.