Journeys within Rostock cost €2.50/5.50 for a single/day pass. The Hauptbahnhof is about 1.5km south of the Altstadt.
Trams 5 and 6 travel from the Hauptbahnhof up Steinstrasse, around the very central Marienkirche and down Lange Strasse to the university.
From the Airport
Bus 127 connects the airport with the city centre (adult/child €9.80/7.50, 35 minutes) at least five times daily; departure times depend on arriving/departing flights.