It's difficult to get to, but the north east of Poland (lake region), especially around Szurpiły is beautiful.. Or if you go to Gdansk the seaside to the west is really nice. The coast in Poland is considered national park and is protected by about a km or 2 of pine forest, so the beaches are really wild (there are also some amazing sand dunes and Europe's biggest "desert") with almost no construction. It's generally about a 1 - 2 hour drive from the city depending on how far you want to go, so great for a day trip. Just keep in mind that you'll have about a 35 minute walk from the car through the forest to the beach if you do go. I can give you some more specifics if you like.
Łódź is very interesting, especially if you like post-industrial cities that are beautiful but run down. Lots of amazing decaying architecture. It might also be worth looking up Katowice, another "industrial" town, by which I mean became rich during the early 1900s, so lots of interesting architecture. It also has quite a thriving art scene at the moment and the city is trying to encourage cultural activity so lots going on.
There are a couple of places around Warsaw that make good day trips that locals do regularly. The 2 towns people usually go to are Sandomierz and Kazimierz Dolny, which are 2 of only a handful of small complete medieval towns in Poland. There's also Toruń, about 3 hours from Warsaw and a good day trip, which is one of the oldest cities in Poland.
There are plenty of places to see, but It kinda depends on what you're interested in really
Film is easy to get in Warsaw, there's a chain called Profilab that has a few shops dotted around the city, but can be expensive. The "best" is
Czarno Biale, which is on the 2nd metro line near Rondo ONZ (United Nations roundabout - which is not actually a roundabout).
But when you're in Warsaw, I would definitely recommend a visit to
fotoplastikon!