Like I said before, last April I stayed at the Holiday Inn on Presidential Avenue/City Line. It's pretty close to Drexel Med, *and* they provided free transportation (tip aside) to the school on interview day.
The ride only took something like 10 minutes. For pure convenience, you won't get much better. The only catch is that it's definitely not downtown. You'd have to take a Septa bus for 20-30 minutes to get there, I think no. 38. The bus stop is right in front of the hotel though, so it's certainly feasible. btw, the Adams Marks hotel mentioned above is almost right next to this Holiday Inn but I'm pretty sure Holiday was slightly less expensive...
If you're set on being downtown and taking the R8 regional rail train to the interview, then I'd suggest something adjacent to Market East station on 8th and Market since it's closest to the historic areas.
btw - City Hall is a subway stop, NOT a train stop (though Suburban station's not too far away). There's absolutely no subway line near Drexel Med.
Finally, 30th St. station where you'll get off Amtrak is sort of middle ground - not downtown but the closest train stop to Queen Lane (forget North Philly), and there's a subway line that goes all along Market Street (you'll want the eastbound direction to get downtown).
Hope this helps, you can PM me if you have questions. btw, here's a link to the R8 route. Again, I really don't know how far you'd have to walk along Queen Lane from the train stop...but I don't imagine it'd be that much.
http://www.septa.org/schedule.cgi?route=r8n&day=1
Bus no 38 route:
http://www.septa.org/schedule.cgi?route=38&day=1