Julie,
Check out the area between North Ave and about 27th Street, along Charles/St. Paul/Calvert streets. This area is known as Old Goucher, Barclay, and Charles North, and encompasses a bit of the southern end of Charles Village. The closer you stay to Charles Street, the better, as some areas west of Charles Street can get a bit rough. Several bus lines run through the neighborhood, and there are plans/talks to extend the free Charm City Circulator should run as far north as Charles Village. You could conceivably commute without a car, completely for free. Also, the neighborhood has a Safeway and some other convenient amenities. Getting renters shouldn't be too tough given that you are between MICA, JHU, and UB.
Ping @Matthew Newcomer. He's got a project going on in the neighborhood, and I think he lives there as well.
Take a look at Reservoir Hill. It's in transition, but you've got great architecture and you are really close to MICA. The area has some blight, but hey, it's Baltimore. You've got pocket parks in the area that might be perfect for you, but you walking around after dark may make you a bit uncomfortable.
Going south to Station North, you have some interesting opportunities. I lived there for a few months and there were multiple pocket parks perfect for dogs.
A multi in Patterson Park is going to be above the price range you quoted. Hampden might be an option, and if you are looking for something with a decent yard, you might consider Hamilton/Lauraville. Some of houses are multi-units or have in-law apartments.
Cheers,
Andy