Very difficult to choose. According to Rick Steves it would be Olomouc. Brno did not make it into his book Prague & the Czech Republic. Olomouc's inner city is the second largest historical monuments preserve in the country, after Prague. It used to be the capital of Moravia until 17th century. After that Brno is the capital. Olomouc is mostly flat unlike Brno which is mostly hilly. Olomouc is the 6th largest city in C.R., Brno is the second largest. It is about 4 times larger than Olomouc. Both are university towns. Brno is on the direct rail line to Budapest. From Olomouc you would have to train to Breclav and there change to train to Budapest. You will be there in December. Both cities have nice Christmas markets. What to see in Olomouc: see the Rick Steves book. In Brno: walk up Masaryk Street from the Main Train Station, stop at the Visitor Center in the Old City Hall, to Freedom Square (namesti Svobody) where is the largest Christmas Market in Brno, then through the pedestrian shopping street Ceska. Then you can go to the castle (or fortress) Spilberk (it's quite uphill). You can also visit St.Peter and Paul Cathedral (it's close to the Main Train Station). If you want to do a tour of villa Tugendhat (it is on the UNESCO Heritage Site) you better book it ahead online. If genetics interest you, visit Mendel's Museum in the abby on Mendels Square. The founder of genetics did his experiments there. If history is your hobby then city bus can take you to the battlefield of Austerlitz where Napoleon beat much larger armies of two rulers (of Austria and Russia). The battle happened in the beginning of December so if you time it right you could see the reenactment. Otherwise there is a museum there and Cairn of Peace. Of course you can find a lot of information about these two cities on google and that also can help you with your decision. Let us know how you decided. I think you cannot go wrong with either of them.