In Shutter Priority mode on your d60 you should be able to slow down the shutter speed to anything as low as 30 seconds to achive a photo like that depending on how much light there is. You can also set the shutter to "bulb" setting and use a remote to activate the shutter open and closed. This way you can keep the shutter open for as long as you want to get the desired photo, as long as the battery doesn't die on you.
Yes, your D60 can do that for sure! Just put the camera on the S mode, and put the Shutter at like 2 seconds or something like that. Get a tripod, and snap the pic. Its gonna take some practice, but i have done plenty of cool night stuff with my old D60.