I’ll be arriving into Gdansk, in Sept., have 5 nights. I’d like a day in Gdańsk, but then on to Warsaw and Krakow. Should I plan 2 days in each or 1 in Warsaw, followed by 3 in Krakow. Krakow sounds a bit more intriguing, plus, Auschwitz-Birkenau is a full day tour. Can I do all this by train?
Yes, you can access all three cities by train - but your timeframe is really, really tight to try to squeeze in all three, and that's not even counting the transport time between them. For a "quality" trip, I would pick two at most and give them 2-3 full days each. Warsaw is the largest and requires the most time, the other two are small and compact. All three have plenty of attractions to keep you busy for at least 3 days (each). Poland is a large country, so 5-6 days is really short.
I would stick to Gdańsk and Krakiw with this amount of time, in fact it’s short for even those two cities. Yes you can do this by train, Gdańsk to Krakow is about five hours though. I visited Gdańsk and Krakow last year and wished I had taken more than seven nights to see the two. I could easily have started with four nights in Gdańsk as it’s such a pleasant city, four nights in Krakow was too few given the first day was spent getting there and we did not arrive until around 6 p.m.
Everything depends on your logistics. If you have to fly into/out of Warsaw, then don't skip it (there's plenty to see there). In worst case, you can do a day trip to Gdansk and still get a decent feel for it. If you choose Krakow and Gdansk, then maybe flying between the two makes more sense (if it only takes 2 hours as opposed to 5 or so via train).