Located in Southern Hungary near the Croatian border, Pécs is Hungary's second-most visited city, and rightly so. It has a compact old town which can be easily explored on foot, with buildings from many epochs (late Roman to 20th century) and religions (churches, former mosques converted into churches, active mosques and synagogues).
The Roman sites are very central and very well signposted (they make a lot of their WH status). There is a brand new visitor centre above the main site, called Cella Septichora. The remains themselves are reasonably interesting (of course nothing compared to Rome, but nice for a provincial town), and show biblical scenes from the dawn of the Christian era in the Roman Empire.
Pécs is connected by direct trains to Budapest and Vienna. Like Christer, I stayed at the Palatinus, which is a really nice and traditional hotel.