I spent 3 weeks in Poland and it wasn't enough! I think a month is a perfect time. Although, I would urge you to pick at least two bases as Poland is a large country and Krakow is just in one corner of it. If you had a full month, I would think to do a week in each of Krakow, Wroclaw, Warsaw, and Gdansk. Most people say to skip Warsaw, but I quite enjoyed it and was sad I only had two days to explore. Its much more of a modern city than the rest and is filled with beautiful parks and good food halls. Poland is really well connected by both train and bus and really affordable to get around. If you buy through flixbus, make sure to buy through the flixbus.pl site and just translate into English because it will save you money! Ticket prices go up significantly buying last minute however the price is never too crazy (ie. An advanced bus ticket from Warsaw to Krakow can cost as little as 17 zloty ~4.25 usd but bought the day before for a Saturday ticket can cost closer to 80 zloty ~ 20usd).
I found booking.com to be much more useful than airbnb (and even hostel world ironically). So I would def check there to find some affordable apartments. I think my most expensive private room was $27/nt with shared bathroom/kitchen (not a hostel but an Aparthotel). I got a private room/bath in a hotel with free breakfast in Torun for only $25/nt. You can see its easy to find affordable accommodations in Poland. You can also easily find affordable food if you do not want to be eating out all the time. There are places called milk bars all over Poland that are a relic from the communist times. It usually a place serving food cafeteria style. Its a no frills restaurant that is often only in Polish (so google translate is very helpful) and the food is usually super super cheap (and its quite a local experience). I went to one in the market hall in Wroclaw and got a plate of 8 HUGE pierogi for 8 zloty ($2) and a plate of their version of crepes with sweet cream for just 9 zloty. My eyes were bigger than my stomach and I should have ordered just one meal.
A few places I think you should check out whilst in Poland: From Krakow you can visit, Zalipie, Auschwitz, the Salt mines, Zakopane (if you're into hiking you must visit here). Torun is a city worth visiting but it definitely doesn't need more than a day. If you make it to Gdansk, Melbork castle is a must and if you go you can skip the amber museum in Gdansk, also everyone told me I needed to take a trip to Sopot but I didn't have to time to make it out there. I took a day trip from Wroclaw to Ksiaz Castle and loved it, but make sure to allot a whole day to it. We arrived mid afternoon and had to rush through.
I could go on and on about Poland, it surprised me how much I enjoyed it and this group was really helpful in setting up my plans. Poland is a great budget option with a ton to offer and plenty to keep you occupied for a whole month.