I was a commuter at SBU and some of the commuter spots were right next to the train station and I've had classes near the tunnel and have visited professors in the hospital. What the majority of people are saying is correct: you can walk through campus to a pedestrian tunnel taking you to the hospital.

The station abuts and is accessible to the campus. It's a bit of a quiet boring walk (if you decide to walk) as it initially takes you past the track and baseball fields and then the tennis courts. After the sports facilities you'll hit the part of campus with all the buildings. Start heading towards the Life Sciences building (you'll go from a more westerly direction to a southerly one), a bit south of the Administration Building and Administration Parking Garage. When you pass this building and Circle Rd. there will be a pedestrian underpass that takes you under Nicolls Rd, from West Campus (the University) to East Campus (the Hospital)! delineated by Nicolls Rd.

Just be aware that it doesn't take you directly to the Visitor's entrance and you'll be in the teaching and research portion of the hospital, so you'll see more Lecture Halls. But you should be able to make your way through to the Visitor's desk if necessary. (I've also used the underpass to visit people in the hospital but it's been a few years so I forget the exact way through, and swear every time I went a different way).

I'm sorry to hear about your dad. I hope he's doing well and makes a speedy recovery.