I am starting a new job in a few weeks, and for the first time ever I feel like I did a good job on the negotiating part.
Basically, I waited until I had a written offer from them (via email). The offer was at a higher salary but with worse benefits (time off, % of health insurance, % of money to retirement, and free child care -- I work at a school that has a summer camp which my son attends for free). I called back and said that while I really appreciated the offer I didn't feel like I could move unless the new "package" was significantly better than my current one. I followed that up with an email that detailed what I have now. They made me a 2nd offer with more salary, more leave (same as I have now), and free before and after care. They also offered me a signing bonus. I'll still have to pay more my insurance and retirement than I do now -- but the difference in salary covers that and still adds about 10%.
I do think it's possible to negotiate these things, but that the point at which it makes sense if after you get an initial offer.
Good luck!