OP doesn't give details but if he's coming in from EWR, you may well run into the PHL passengers at immigration, plus whatever charter flights there are so don't bank on having a quick trip through.

You could go into Birmingham but assuming 45 mins to get through formalities, 5 mins over to the station, 10 mins for a train then 20 mins into town, you'll have time to have some breakfast and a quick look around (there are some decent shops as well as the horrible mall ontop of New Street station) before needing to get back out to the airport. If it's an 11am flight then you need to be on a train from the city centre at 10am at the very latest, as queues for T2 security seem par for the course.

All told, i'd just get a decent book and seek refuge in that. There's a Novotel on the airport complex - never had breakfast there, but have eaten in the chain's other UK properties and it's a decent spread.