The most common and most likely answer to this crossword clue is the 5 plus 7 letter word SAINT ANDREWS
I've seen this crossword clue in The Sunday Telegraph
S
A
I
N
T
A
N
D
R
E
W
S
Buddy explains!
The straight part
We know that "Location of university/that has courses old and new/of good character" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case location of university/that has courses old and new/of good character = saint andrews.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.