Before deciding on the direction, please perform the below steps to demark the exact zones. Take the plan of the entire building including the compound wall. Place a 3x3 grid on it. This will give you the exact zone of the Building plot. Once this is done it gives a clear picture as to which zone has Stair case or Underground tank. Since you are thinking of the second floor flat, in this case the ground energies matter a lot.
IF you have already done the above excersise
As per vastu Shastra, the North and east should be lighter, where as the South and West should be heavier. Underground water tank is a form of cavity which reduces earth element. SE being the direction of Fire element water in this direction creates a imbalance. Also as you said stairs are in the NE, that is addition of excessive Earth element in the source zone (Zone of water element). So as per your description two zones of the vastu are already impacted and since this is a apartment you cannot change the UG tank as well as the stair case.
My suggestion here would be talk to the inmates of the other flats residing in this building and know their experience before making a decision. Also the impact will not be immediate this will be over a period of time.
Pavan Matkar (firstname.lastname@example.org)