Negotiating between schools is common and accepted. Be respectful, but you are well within your rights to ask either school for more.
I see you are deciding between Syracuse (#96) and whatever #125 is (there is a 7-way tie for #119). Based on proximity, I'm going to guess Vermont, Maine or Drexel.
Here's the thing about USNWR. The rankings are pretty arbitrary and schools between 50-200 shift around like crazy. Once you get into that point, rankings pretty much stop mattering. Will going to school ranked #50 look better than school ranked #200? Maybe, but it shouldn't be your primary concern. If you aren't going to a school with a national name (read: the T14), you should be focusing on three primary characteristics: Location, Employment Stats, and Cost, in that order.
No schools outside the T14 have a nationally portable name, so depending on the market and the school, you shouldn't expect your degree to travel further than the states surrounding yours (and lots of times, not even that far). Go to school where you are planning to work. That means if you go to Syracuse, you're hoping for NYC but have a real shot at being stuck in upstate NY. If you go to Drexel, you're hoping for Philly, etc.
2. Employment Stats
This is just as important as location. Make sure you know your odds. Syracuse only gave the class of 2011 a 50% chance of getting a job as a lawyer. Look at the link below and you will see only 50.3% of the class got long-term, full-time legal jobs 9 months after graduation. The nature of legal hiring is such that if you do not find a legal job within a year, your odds of ever working as a lawyer start dropping significantly. http://www.lstscorereports.com/?school=syracuse&show=chars
It is tough to evaluate your other options, but you should assume that any school ranked at #125 will give you between a 30-60% chance of finding full-time, long-term legal work. Look at the NALP data on www.lawschooltransparency.com
to get an idea of the kind of outcomes you can expect from your options, and plan accordingly.
Because you stand roughly a 50% chance of finding work, it is of utmost importance that you do not take out loans for your schooling. Legal salaries are bimodal, meaning even if you find a job, you will most likely be making between $40-60k (at MAXIMUM) upon graduation. In general, the jobs paying $120-160k are at Biglaw firms. No school outside of the T30 places more than a few percentage points into Biglaw, so you cannot expect that as a realistic outcome.http://www.nalp.org/salarycurve_classof2011
Ideally, you should not go to either option for more than free. If you are taking out loans, you should pay AT MOST $60,000 including living expenses, fees, interest, tuition increases, etc. Because of the poor job prospects coming out of T2-T3 law schools, and because of the bimodal nature of legal salaries, it is very important that you mitigate your risk.
Additional information would also help. Where would you like to work, and what do you want to practice?