hey guys,
I've been living in philadelphia (west philly and currently center city) for the past 6yrs and I've found the city constantly stimulating and affordable, very rare. If you want to live downtown (appx 15-20min from queen lane), you will have to look pretty thoroughly to find a decently priced studio/1bdrm. I have been living at 1530 spruce st. (great location) in a 2bdrm for 660$.mo-very reasonable-my bldg is far from the nicest in the area, but very livable. Overall, cheaper bargains are hard to find downtown but quality of life/access to culture/entertainment are at your doorstep. Personally, i've enjoyed the distractions of living in a large city and i'm leaning toward staying in center city through medical school. also-shuttle/regional train service are very closeby.
sorry, i can't really speak to the area surrounding drexel with the exception of manayunk which is an affordable, hip area within a 5 min drive. After scanning rents online, it seems that the queen lane area has some really cheap 1bdrm options (350-600ish).
safety isn't a major concern in center city (one of the safest areas in phill) and the area around drexel med seems pretty safe/charming, nothing blighted and shacked up as is the case surrounding temple u in north philly.
hope this helps,
Biff