Eastern Germany 5 days - trains or car?

Pirna and Meissen are both on the S-Bahn network with half-hourly services from Dresden Hbf. Görlitz has also a more or less half-hourly service. Check at http://www.bahn.de/p_en/view/index.shtml

Unless you are going into deep rural areas, train and bus are fine and are used to tourists. Around Dresden, regional bus and train tickets including much of Saxon Switzerland are on the VVO site. Further east check out ZVON.de for bus and train times and tickets around Bautzen, Görlitz and Zittau including travel into both Poland and Czech republic.

Thank you both. Can we book trains locally or should we do it in advance?

These are short rides without any need or advantage of advance booking. Buy the tickets at the station the evening before to avoid the risk of missing your train when there is a queue at the counter.

Thanks Tonfromleiden

Decades ago there used to be a ferry boat up the River Elbe from Dresden to Meissen. If it's still there it might make a nice change from trains and buses.

Some things stay forever: https://www.saechsische-dampfschiffahrt.de/en/ (I'm not a native speaker, but I thought that with the recent spelling reform it should be written as »dampfschifffahrt«.)

The only journey where booking un advance might be an advantage is Berlin - Dresden and return in case there are some deals using the Intercity trains - might be worth a look 2 - 3 months before you're due to travel. Alternatively, check out the fast growing inter-city coach network - I know BerlinLinienBus do Berlin - Dresden and I think Flixbus even do Dresden - Goerlitz.. And don't forget Deutsche Bahn do regional tickets - the Saxony one includes Sachsen Anhalt and Thuringen and can be found at http://www.bahn.de/p/view/angebot/regio/sachsen/sachsen-ticket.shtml?dbkanal_007=L01_S01_D001_KIN0014_lt-sachs_LZ01 but I think if you search you'll find an english language version too There really are anumber of bargain tickets to check out, just needs you to decide which suits you best.

Sorry, I forgot the trip from Berlin to Dresden. On cheapest train EUR 40; Sparangebot for EUR 19. It clearly pays to have those advance booked. A regional ticket for Görlitz is also much cheaper than two tickets at the normal price, but those don't need advance booking.