The Bloomberg School of Public Health is on the Wolf Street Campus - you will probably not be living any where near East Baltimore (Unless there is Medical / Nursing / Public Health housing that I am not familiar with). Many of the Hopkins and UMD students reside in the Hampden and of Course Charles Village and Abell neighborhoods. I would caution against Remington, but there might be some decent living opportunities there. There are those who love Federal Hill, Fells Point, Canton, Bolton Hill, etc, but the commute and living conditions would require research - all of these neighborhoods are very different. I personally would highly recommend Charles Village. Particularly in the following areas: North of 26th Street and South of University, East of Charles Street and West of Guilford. There are lots of apartments, students, and things to walk to in that area and the neighborhood is large and diverse. Hopkins runs a shuttle to the Wolfe Street campus, and then there is the city transit.
Crime in Baltimore is extraordinary, and your lifestyle should reflect the increased risks that living there would entail; however, Baltimore can be a great town. I would not let that city's issues prevent you from attending JHU if that is where you are leaning.