There aren't any hotels near Hopkins. Nobody in their right mind would build one over there either, it's a horrible neighborhood (although with JHH buying up all the property and trying to turn the area around, this may eventually change).
Get a hotel down near the harbor. You'll be much happier that you did. (And it's only 5-10 minutes from the harbor to the hospital, depending on how many red lights you get)
Drive time from BWI airport to JHH is about 20-30 minutes, depending on time of day- morning rush hour will be worse, since 395 is the only main road into downtown right now that doesn't have construction going on. I-195 to I-95 north, I-95 to the exit at I-395 north, stay on 395, do not follow the exit for MLK Blvd, right on Pratt St (2nd light), left on Caroline St, right on McElderry St, park in the garage on the right (that's the only visitor garage at the moment while a bunch of construction is going on). These directions are a little easier than the directions on the JHH web page.
Maps and Directions to Johns Hopkins Locations
Call guest services, I think they have special rates set up with local hotels. 1-800-225-2201
Johns Hopkins Hospital Patient Information