Season 1 - Episode 2 - "Paternity"
The body of water shown in the opening is actually Lake Carnegie, which you must cross to get into Princeton when traveling from the east-southeast. In winters when the lake froze, people would come from miles around to go ice-skating. I had a lot of fun skating there. (It was free.)
It's typical to see sculls on the water. If you look at the far shore, towards the background, you can see the University boathouse through the trees.
I don't ever recall knowing a name for that particular bridge. It may have had one, but I never heard of one. We just referred to it as the Washington Road bridge. Washington Road runs from Princeton Junction to the heart of the Princeton University campus.
In the scene with House and Foreman, during the search for Dan, they're talking in a corridor. If you look at the double doors, you'll see "Witherspoon Wing" above them. (It's a bit hard to read in this scene.) Witherspoon Hall on the Princeton University campus was named for John Witherspoon, the 6th president. It is the oldest existing dorm. 253 Witherspoon Street in Princeton is also the address of the real Princeton Medical Center upon which PPTH is based. (BTW, Plainsboro is a real town a short drive east of Princeton.)
I was tickled that the clinic patient was from Maplewood, a very wealthy town in northeastern New Jersey. I went to college near there. You could get finger sandwiches and a pot of tea at the Lord & Taylor's there for $1.50. A lot of us college students went there for a delicious, cheap lunch. In reality, Maplewood is only about 40 miles from Princeton, not 70 as House says.
Later on, when House is talking to the clinic patient and they're walking through the double doors, you get a good look at the words "Witherspoon Wing." They then stand in front of another set of double doors over which it says "Mathey Wing." Mathey College is part of Princeton University. It was dedicated in 1983. It's one of five underclass residential colleges.