I lived there for four years before I moved to the UK and am shortly to marry my Czech partner, so know a bit. Unsurprisingly, I love the place and would never have moved to the UK if it weren’t for what appeared to be better job opportunities at the time.
As above, you can survive speaking only english but once you are out of Prague or other major tourist towns you will struggle. When I first moved there I lived in Ostrava in the far east of the country and very few people in shops etc spoke any english. However many younger people do, as they now generally learn at least something in school. I guess it really depends what your expectations are, how long you are going for and where you are going as to how much Czech you’d want to learn. It’s true that in some ways it’s very difficult (very complex grammar) but in other ways it’s fairly simple (completely phonetic, consistent application of grammatical rules). Certainly learning a few words to get by is not the end of the world – having a meaningful conversation is another matter.
Anyhow, a couple of recommended places to visit other than Prague. Karlštejn is a lovely old castle (there are loads of castles – something like 2000 across the country) just a short distance from Prague. ?eský Krumlov is beautiful but a little touristy. Olomouc is my hot tip for beautiful Prague-like architecture but without the tourists. As for nice mountains etc ?eský ráj (czech paradise) is less than a couple of hours from Prague and is simply stunning. Both the šumava and Krkonoše mountains in Bohemia are lovely, especiallz šumava. The east of the country is also a very interesting combination of heavy industry with some beautiful natural landscape. Well worth going to the Beskydy and Jeseníky mountains if you have the time.
If you have any more detailed questions just fire away.
Yes, you will have a good time!
P?eju t? p?knou dovolenou!