The Czech Republic lies at the center of Europe, surrounded by Slovakia (which it once was joined with to form Czechoslovakia), Austria, Germany and Poland. Architecture, from what I've seen of Brno and heard of Prague, has much in common with that of elsewhere in the former Austro-Hungarian empire, which means that it's beautiful. The Czech beer is also regarded amongst the best in Europe - having tasted plenty of it, I'm certainly in agreement there.
In the (for most people quite unlikely) event that you speak or understand some Slovak, getting by in the Czech Republic shouldn't prove much of a challenge. On my first trip there I just spoke in Slovak, and for ordering food and buying museum tickets it worked out just fine.
That said, some words are completely different rather than being the same or close enough to be obvious, and while I could understand enough of what was being said to me by people, the difference in rhythm and pronunciation was obvious to hear. However similar you may or may not find them, they are classed as distinct languages, and you can probably offend some locals by suggesting otherwise (equally, other locals will agree with your viewpoint).
While I spoke in Slovak because I wanted to have Czech spoken back to me so I could hear it and maybe learn a thing or to, it appeared that getting by with English in at least cities wouldn't be a problem. Announcements of international trains at train stations were made in English also, at least at Brno. I expect you can find a good number of people that can speak German too.