No, the maximum federal benefit rate, currently at $733, does not change depending on where you live. However, most states do provide a small 'supplement' to SSI, at the state level, and this amount, varies by state. That said, it is often recommended that if you have fallen on hard times, and are disabled and can't work, (but have not bought the disability insurance that would have provided you with Social Security Disability Insurance Benefit more commensurate with your work efforts/payments), and are depending on welfare such as SSI, that you tailor your budget to live better within your limited means. For instance, you may be better off living in a more moderate to low income area, that your limited welfare income can pay for more easily, so you leave more of your income in your pocket for other monthly needs.
Also know that even though you are on SSI, you can generally work a little, and earn a little, each month, to increase your financial wellbeing each month. If you have more questions on that, feel free to use our Affordable Q&A service, so you can inquire more specificially and get one on one answers to your questions about working when on SSI.