1) Princeton U

its link with the town of Princeton is not strong and it had a woman college:

Originally founded at Elizabeth, New Jersey in 1746 as the College of New Jersey, it was relocated to Princeton in 1756. In 1887, the university had actually maintained and staffed a sister college in the town of Princeton on Evelyn and Nassau streets, called the Evelyn College for Women, which was closed after roughly a decade of operation. After abortive discussions in 1967 with Sarah Lawrence College to relocate the women's college to Princeton and merge it with the university.

2) NYU
On April 21, 1831, the new institution was officially incorporated as the University of the City of New York.
Founded in 1831, New York University is the largest private university in the United States. The University operates branch campus and research programs in other parts of the United States and abroad, as well as study abroad programs in more than 25 countries.

3) Boston U again was not originally founded in Boston and did not have strong link with it.

On 24-25 April 1839 a meeting of Methodist ministers and laymen from throughout New England was held at the Old Bromfield Street Church in Boston. This meeting voted to establish a Methodist theological school. The school was established in Newbury, Vermont and was called the Newbury Biblical Institute.

In 1847 a Congregational Society in Concord, New Hampshire, invited the Institute to relocate to Concord and made available a disused Congregational church building that was able to seat 1200 people. Other citizens of Concord covered the remodeling costs. One stipulation of the invitation was that the Institute remain in Concord for at least 20 years. The charter issued by New Hampshire for the relocated institute named it the "Methodist General Biblical Institute", but it was commonly called the "Concord Biblical Institute."

With the agreed twenty years coming to a close, the Trustees of the Concord Biblical Institute purchased 30 acres on Aspinwall Hill in Brookline, Massachusetts as a possible relocation site. The Institute moved in 1867 to 23 Pinkney Street in Boston and received a Massachusetts Charter as the "Boston Theological Institute."

In 1869, three Trustees of the Boston Theological Institute obtained from the Massachusetts Legislature a charter for a university to be called "Boston University." These three were successful Boston businessmen and Methodist laymen, with a history of involvement in educational enterprises and became the Founders of Boston University. They were Isaac Rich (1801-1872), Lee Claflin (1791-1871), and Jacob Sleeper (1802-1889). (Today, Boston University's three West Campus dormitories are named after them.) Lee Claflin's son, William, was then Governor of Massachusetts and signed the University Charter on 26 May 1869 after it was passed by the Legislature.