Is there a way to store suitcases at pudong airport for 2 nights?

Yes. The locations of left-lugagges counters are the following:
T1: between Gate 4 and 5, 10 and 11 in the Departure Hall; between Gate 6 and 7 of the greeting area in the Arrival Hall
T2: near Island A and M in the Departure Hall; near the International exit in the Arrival Hall
You can easily find these places according to the detailed English signs at the airport. Don't worry.