Someone recently made an AMA with some of his advice on polish version of reddit.
If you know someone understanding polish that should be much help. I've never really researched the link from above, I could help you a little in understanding what the guy wrote in the link, but I suppose you can even try translator first and I maybe I could help from there. Anyway the guy in link recommends first to find any documents you have, ask anyone of the family anything they could remember (like grandpa had sister Ania or Anielka who was born around 1890, anything really) and start from there. Religion could also be important, as up to some point a lot of documents were being made by the priests, pops, rabbis etc.
From what I see there is site you can easily use as english speaker, here:
Always remember in polish women often have "a" instead of "i" in the end of family name, so it's good idea to always make to searches - "Piechowski" , "Piechowska"
From the link below I've learnt there are more then 100 people of Piechowski/Piechowska name in the biggest city nearby (less then 60km), so they could have easily moved there (or anywhere to be fair) - since 1905 or even 1950 a lot of people moved from villages, small towns into the city.
As you can see above there are more then 3000 Piechowskis in Poland right now (not sure how accurate this is), so that shows how much information there is if you won't narrow your search enough.
Answering to your question about moving from one side of the country to another (it doesn't look like it is far in this case though): there could be plenty of reasons and that wasn't that hard really. Sure, wasn't as easy as today, but don't undermine the possibilities of those times. In my family history I could find one example of several families from one village moving far further distance, because goverment was trying to move more people into low populated area and they encouraged people to do so and promised much more land there. They just put everything they had on horse carts, with a lot of children and just rode for quite some time (probably several days).
And by the way, there was no Poland up until 1918. Everything belonged to Russia, Prussia or Austria.