Yes, Nemec means German in Czech; Nemecek is the diminutive -- 'little German'
Brno and Znojmo are in the Moravian area of Czechia -- South near Austria border.
Also check out these sites: www.czechfamilytree.com/regarchives
Clicking on the Mesta.obce logo brings up lists for counties, cities and towns of the region which are searchable. There are homepages for each local government giving contact information, history,statistics, tourist information, photos and useful links. In Czech - you'll have to use a translator if you're not fluent in Czech.