There may very well be options for you at that budget, but you may not know where until you actually get further into the admissions process. Let me break your question down into two parts, the cost of tuition and fees, on the one hand, and living expenses, on the other.
The problem in matching an LLM program and personal budget upfront is largely due to the uncertainty of what your real tuition costs will be. Every program, of course, tells you what their announced "sticker price" tuition is. (An easy reference to compare "sticker price" tuition can be found by going to a program's profile here on llm-guide and clicking the table icon next to their current tuition.) However, many programs offer scholarships or tuition waivers that may reduce your real cost of tuition. To the extent that these are awarded on the basis of merit, you are unlikely to know whether you will be awarded one or for how much until late in the term preceding the start of your LLM program.
You can, of course, get a good sense early in your research of the relative non-tuition expenses of attendance at different programs by researching relative cost of living indices (e.g, the cost of living wizard at salary.com), going to Craigslist or realtor.com to see what apartments rent for in the neighborhood of your preferred law schools, etc.
Once your admissions and - hopefully! - scholarships offers have all come in, compare the total net costs for each program. When comparing the relative economics of different programs, try to be Mr. Spock the Vulcan -- you may feel program A is a "better" offer because they gave you $30,000 and program B only gave you $10,000, but for this part of your decisionmaking process that shouldn't matter if the total net cost of a year in program B is less than than the total net cost of a year in program A.
Good luck with your planning!
(Full disclosure - I am the Executive Director of the Pitt Law LLM program.)