Without the use of a tripod, you're going to have troubles but good techniques will go a long way.
Can you use a flash? How about a monopod? Sometimes shots with motion blur can be very interesting. Do you have a lens with Vibration Reduction? That would come in very handy. Kind of looks like I'm rambling here doesn't it.
If you are taking shots to highlight the bar/club, does it really matter that the people in the photo have motion blur? I ask all these questions because these are questions you should be asking yourself.
What are the ultimate goals of these shots I'm taking?
Now, for technical stuff. With the D60, I would probably raise my ISO to 400 or 800 in a pinch. Raising your ISO from 200 to 400 is one full stop, so you'll be able to increase your shutter speed by one full stop(1/60 to 1/120). I wouldn't use "Auto ISO", this is just asking for trouble. Set your camera to "Aperture Priority". This will let you set the desired Depth-of-Field(DoF). Remember, the smaller the f/number, the smaller the DoF & the faster the shutter speed.
This obviously is just a starting point for you. You could go out and take a test shot using what you have learned here so far, come back here & post it & we could help you improve you next shot. Remember to post your EXIF !!!