This is an extremely easy and fast commute...that's the good news. The bad news is the Old City area is actually brutal on bike thefts and mischief. I had a pump stolen off of my bike at 2nd and Chestnut...right outside Khyber...and you're going to be dealing with a lot of drunks and rude, loud, drugged out club schmucks during those hours. Old City is rapidly becoming like South Street was 10 years ago, a mixture of frat boy and ghetto clubs and bars.
I would recommend parking the bike closer to market or near the parks. I also wonder if you need to take a cab as it's about a 30 minute walk or a 5 minute ride on the Market Frankford El...which runs all night as a bus.