Law School
From a Tulane law grad- If finaces aren't an issue, the real question is what are you interested in? If you have ambitions of a more nationalized practice (federal laws like ERISA or civil rights or con law, etc.) or envision leaving Louisiana, Tulane is probably the right choice.
If you envision a general practice in La. or a practice that does a particular kind of law that is state law (personal injury, land/property, family law or trusts and estates) both Loyola and LSU are excellent choices. Loyola might be more beneficial in the immediate NOLA area and LSU for the rest of the state. (But that's no "rule" by any means). Since you said Lafayette, LSU might be the right call.
Also, there are specialties. If you are interested in maritime or environmental law, Tulane is exellent in those areas. But LSU and Loyola excel in other areas.
The nice thing is that all three are good law schools- so you can't really go wrong. Another thing to remember, though, is that LSU is very competitive within your class. Unless things have changed, they actually "drop" a percentage of the class after the first year. So if it takes you a while to "get it" in law school (some people take longer, but eventually most everyone gets it) you might find yourself struggling to stay in LSU.
Loyola and Tulane aren't like that. Get in, pay your bills and unless you fail out, you'll be able to continue.
IMO.
Good luck with your decision!