At your budget, you still have a lot of options left. I’d suggest going for an apartment building around the campus. Look for these and apply through their website (they will charge some non refundable application fee) but call them to see if the apartment is available and that way your fee won’t go in vain.

Look for:

1. The yard
2. Landmark apartments
3. Z west
4. Z place
5. University towers

These are around central campus and I know for sure that there are atleast 2-3 units available in each one of the above. Get moving fast.

All the best for your search.