Academic Transfers - SOLUTION

 Spoilers below!

This was a tough one! 

The first observation is that there are three colleges/universities in the grid: LAKE FOREST, IONA, and DEPAUL. What do these three have in common? For all three, you can change one letter obtain a different college:

• 18A LAKE FOREST --> WAKE FOREST
• 35A IONA --> IOWA
• 52A DEPAUL --> DEPAUW (my late grandfather's alma mater)

Not only that, all three substitutions involve a W. Could WWW be part of our answer, perhaps?

The second observation is that each of those substitutions results in the crossing Down entry forming a new legit word or phrase:

• 5D MY LORD --> MY WORD
• 24D IS NEAR --> I SWEAR
• 25D THE GOOD LIFE --> THE GOOD WIFE

The first letters of those spell MIT... another university! Coincidence?

The final observation is that each of those new crossing entries can also be the answer to a clue somewhere else in the puzzle:

• 17A ["Good heavens!"] = EGAD, but also MY WORD
• 23D ["You'll have to trust me on this"] = DON'T ASK, but also I SWEAR
• 34D [2000s-10s series whose title role earned an Emmy for Outstanding Lead Actress] = UGLY BETTY, but also THE GOOD WIFE

Taking the first letters of those entries in the grid gives us EDU. 

Putting it all together, we get WWW.MIT.EDU, our final answer, which is indeed a site of higher learning.