Answer is 4. Both India and UK
Here's How :
Total number of visitors from India are 3 and 4 are from UK.
India on Day 1 has 1 visitor which could be from University 1,2,5,6 and 7. On the second day India has two visitors, one could be from University 3 and other from University 8. So three distinct universities can be covered.
UK has 2 visitors on Day 1 which could be from Universities 1,2,5,6 and 7 and 2 visitors on Day 3 who could be from University 4 and 6. Even if Visitor from University 6 is common, the other three must be distinct because University 6 makes only one visit on Day 1.
Other countries cannot host three distinct Universities because they have less than 3 visitors.