Welcome to C-M!
Where you are from and what your takes are will determine where you'll like to live. Here are three places to take a look at and some others to avoid. Also, know that Cleveland has a new free trolley that runs from the center of downtown (Tower City) to the law school. Plus, the you'll get a free bus pass so feel free to expand your search (although, other then the trolley, Cleveland public transportation SUCKS).
1) My friend just moved into Statler Arms http://www.statlerarms.com
The halls are clean and the apartments are very nice. Take a look.
2 & 3) Huron Square and The Osborn are nice clean building within your price range.
Be careful, but perhaps take a look...
Right across the street from the school are the Euclid Lofts. They can be small and expensive
but if close is what you are looking for, you can't beat it. Know that if they know you are a law student they will charge you the maximum amount of rent the school allots in your loan package (total rip).
Reserve Square is ok. But you can find better.
STAY AWAY... STAY AWAY!!!
Moving further downtown. Avoid the Chesterfield
. Two friends have had to void their leases and move in the middle of the semester because of their roach problem.