There's really no need to overlap focal lengths if you can help it; it just adds to the weight you're carrying around, so it makes more sense to bring the longest one. I also have Tokina 12-24, which is an awesome lens. I'm trading out my Nikon 18-55 for something more like a 24-70 or 24-85, but I've mostly traveled with those two lenses and been very comfortable with that. I also have a Nikon 35mm 1.8, which is a wonderfully fast lens. If your 60mm is faster than the zooms, it would make sense to take it for use in low light, night shots, or for shallow DOF shots.
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