A trick I learned on this forum: Go to the Wikipedia page of any airport (here's Warsaw's) and you'll find a chart showing all the destinations you can reach by non-stop flights. You have to be careful about seasonal flights; much of your time in Poland will probably fall outside the "season". In addition, any of the listed destinations might turn out to have less-than-daily flights. But this should get you started.
Skyscanner is a good source of information for intra-European flights. You can use it to determine whether a particular destination will have the Friday/Sunday service you'll probably need. I'm not sure all the flights for even next September will be loaded yet. For non-seasonal flights you can probably get a fair idea of the schedule situation by looking at March 2019.
Although you don't necessarily have to limit yourself to non-stop destinations, connecting flights will probably not be very affordable, and they'll really eat into the time you have at the destination when you're going somewhere just for a weekend. If you buy when tickets first go on sale, many of the non-stop destinations will be very inexpensive. You'll need to use a small, lightweight carry-on bag, but that shouldn't be a problem for a weekend trip.
I'd look first at the seasonal destinations to see whether there are any I'd especially like to get to, then I'd see whether I could cram them into the very early part of my stay, since they won't be available options for long.
I'm probably atypical on this, but I'd tend to prioritize places that are small enough that two days would get me close to covering everything of interest to me. So I'd prefer (for example) Lyon to Paris and Zagreb or Ljubljana to Vienna.
Of course, you'll want to get as early as possible a look at the academic calendar to see whether there are any long weekends to take advantage of. A four-day weekend would make a place like Rome or Paris a lot more attractive to me.
Setting aside weather considerations (there's a reason why I travel to Europe between May and September) and airline quality (I, personally, don't fly the tiny ones), these are places I'd consider for a 2-day weekend:
Bari, Basel, Belgrade, Bergen, Catania, Corfu, Dubrovnik, Larnaca, Ljubljana, Lviv, Malaga, Malta, Odesa, Palma de Mallorca, Pula, Riga, Split, Tallinn, Turin, Venice, Verona, Zadar, Zagreb.