You can travel downtown by bus. The number of the buses are 8, 18, and 8E.
The schedules are available on the http://kaposbusz.hu/menetrendkonyv/ website.
(For your information: there are 12 stations – 9 stations, if you travel by the bus numbered 18 - between the University and the final bus-station in Kaposvár)
You may travel by taxi too. The companies in demand are:
City Taxi: +36 82 333 333
Kapos Taxi: +36 82 488 888
Tele Taxi: +36 82 555 555
Euro Taxi: +36 82 666 666
From Budapest to Kaposvár you can travel by train or by bus.
Train schedules are available on the http://elvira.mav-start.hu website. The trains start from the Keleti railway station or the Déli railway station in Budapest.
Bus schedules are available on the www.menetrendek.hu website. The buses start from the Népliget station in Budapest.