cosmosis is right that usually stipend is scaled with cost of living. However, there certainly some places that made offers that even adjusting for cost of living are disproportionally high. If I looked at the range of the offers I got, there was one that was twice as much money before adjusting for cost of living. The one offering more money was in small town upstate New York and the lower stipend was in an expensive coastal city, so the difference in adjusted cost of living would have easily been three times as much. Grad students bought houses at the upstate New York school.
However, most of the time, the differences are not going to be that high. And even when it is, I don't think it's a good idea to use "maximize funding" as a major deciding factor on where to go. For me, I think you need to at least have enough funding to not worry about money on a month-to-month basis because that extra stress is toxic. But after that, it's usually far better to look for better fit or other factors instead of the most money.
But there are always exceptions. Maybe you have extremely high expenses, e.g. medical expenses for you or someone you support. In that case, if a high stipend is necessary for you to even to be able to go to grad school, then that's a different story! This still fits in with the idea that money stops mattering when the funding reaches the minimum you need. Just acknowledging that some cases have much higher minimums.
Finally, in case you really need these high stipends, I found two schools tend to provide stipends that are generous considering the cost of living of the area: Cornell (Ithaca, NY) and U. Arizona (Tucson, AZ).