I would try booking the Hyatt Place 17th Street on Valuetrips.com (legit site, lots of people on Cruise Critic use it). They have free shuttle from the airport. Then I'd pay for a taxi to the port, which is right down the street basically. From there it's only $10-12 plus tip, I believe. That is a safe area w/ lots of restaurants, Total Wine (in the Harbor Shops) and I think CVS and Walgreens. I got a mani at a place down from the Total Wine while my sis and her BFF got massages at the Massage Envy.
There is also an Extended Stay Deluxe in the same area that gets good reviews.. If you can save enough on the hotel, you could pay for a taxi from the airport, too.