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Basically the center is around the "Grote Markt". On this square you will find the Town Hall, Saint Peter's Church and a great place to sample typical Belgian beers. Plenty of pubs etc. can be found at the "Oude Markt", just next to the Grote Markt.
There are accommodations in that area or not far from there. If you arrive by train, you can also consider to stay next to the station. Thus you won't have to carry your luggage very far. The station is only a 10-15 minutes walk from the main watering holes.
On this map, you will see a yellow circle road. In a larger sense, everything inside this circle could be called the "center". It is the historical city of Leuven. Crossing this circle by foot takes more or less 20-30 minutes.