If you listened to Reilly, then you know that the only way to get to The Statesmen Hotel is through a few subway stations. You should still have the series of waypoints on the map. Just follow through the standard subways until you pop out in Vernon square. The streets should actually be clear and the hospital is in plain sight down the right side of the road.
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Go up to the doors and head inside Our Lady of Hope. After that, I can't help much. There will be leveled super mutants in this area, although they should still be on the weak end of the spectrum. I only saw normal mutants and super mutant brutes in the hospital. There's no trick to this one though. Just go around with a hunting rifle or whatever your weapon of choice is to blow away all the super mutants. Stay alert when turning corners and watch the sides. There are a lot of rooms lining the hallways, so it's easy to get ambushed.
As a side note, just about each room has a first aid kit with some stimpaks, so it's worth your time to explore a bit. Other than that, it's a standard clearing mission until you get to the stairs. They are over to the side of the cafeteria area with a lot of super mutants. You'll probably get to it as you finish your walk around the building. Go up and fight through another brief floor in the spots overlooking the cafeteria. Then get up another set of stairs to our goal floor. You should be able to get out onto the “bridge” and cross over to the Statesman hotel. When you get to the end, you have to drop down and enter the second floor of the Statesman Hotel.
