The university in the drama is Kyung Hee University and Seokyeong University.
This is a picture of Kyung Hee University from wikipedia (worth going during cherry blossoms season).
Scene filmed in Kyung Hee University (Source)
And this is filmed in Seokyeong University (서경대학교). (Source)
The concert hall where Seonjae held his first concert with the orchestra is Incheon Culture and Arts Centre. (More information here.)
And the restaurant where Hyewon and Jo In Seo discussed about sending Seonjae to Germany is Cafe M. It is the place marked in the map below, the metro station above is Samseong Station, the orange ones are Daechi Station (left) and Hangnyeoul Station (right).
Address: 서울 강남구 영동대로 315
And on the map below, the station is Apgujeong station and the restaurant is the place with a circle mark.
Address: 서울 강남구 선릉로 152길 33
Phone: 02-544-4081, www.buonposto.com