I think as a general rule, northern Europe will of course more likely feel cooler, especially in late October, vs. southern Europe. So maybe begin the trip in Poland and then travel south?

Re: museums, in less-touristed areas, seems like Nov-Mar museums more likely closed, or maybe only open weekends for limited hours. But for large cities and warmer climes shouldn’t be much a problem.

www.wizzair.com might save you some travel time (and money?).

For transatlantic flights, most airlines shift to shoulder season pricing in September, and then shift to off season fares in November. So October should be cheaper than a summer fare, but September might be better weather if you could shift your outbound to one month earlier.

If you have an .edu email addy, see www.studentuniverse….
Otherwise, www.statravel.com
Open-jaw, meaning arrival at, say, Krakow and return from say, Rome, would save you a lot of backtrack time. However if you get a really cheap roundtrip to Paris or Rome or Warsaw, might be worth it just to add a hop back to Poland with Wizz Air at the other end of your trip.