Don't count any chickens. Many lawyers started out their second summer planning to get offers, and did not. Or had offers rescinded. Depressing, unfair, unexpected, but true.
I would try to find a short term, summer only, downtown solution. Perhaps a crash pad with a few other summers, or an Air b-n-b 12 week arrangement? (That's what I did, I lived with someone in their spare bedroom for the 12 weeks I was a summer. I saved about $1,000 a month on rent + furniture issues, which made me glad when they no offered all summers at the end of the summer!)
It doesn't have to be a pleasant place you plan to spend time in. As a summer, you can expect to be in your apartment from about 8pm to about 7am each day.
Then, IF you get an offer and IF you accept it, I would live with your parents while studying for the bar. It seems that firms are starting people no earlier than September, and as late as January. Between the July Bar and your start date, you have plenty of time to find a place and move, while saving on rent for May to September.