Traveling to Czech republic is safe and easy. Although considered Eastern Europe by the rest of the world we are pretty much (apart from the occasional pothole on the road) a first world country. There are no surprises or culture shocks which you should be afraid of.
The best airport to fly into is Prague (PRG) but if you can get better rates to nearby airports, such as Munich (MUC), Vienna (VIE) or Krakow (KRK), getting to Prague is easy as well. Alternatively you can get to Prague by bus or railway from pretty much anywhere in Europe.
Before you start your journey you should make sure that you do not need visa for entering Czech republic. Here is a list of countries exempt from visa requirement and here is a list of countries whose citizens are required to have a visa. Although getting a visa should not be a problem, some embassies take their time to process the request. Take that into account in your plan!