Warsaw's districts really are different from one another, and the river is the dividing line: the rebuilt west bank has the sights, the east bank has the lower rents.
Śródmieście — the centre and the Old Town
Everything on foot: the reconstructed Old Town, the Royal Route down Nowy Świat, the Palace of Culture and both main stations. It is the priciest base and the least characterful at street level, but you will barely need a ticket. Rooms facing the Old Town Market Square are noisy from May onwards.
Powiśle — under the escarpment by the river
The strip between the centre and the Vistula, with its own rail station and its own bar culture. Students, the Copernicus Science Centre, the university library roof garden and the river boulevards are all here, and it is ten minutes uphill to Nowy Świat. The best compromise on a first visit.
Praga-Północ — the east bank
The district the war largely spared, so the tenements are original rather than rebuilt: brick courtyards, backyard shrines, ex-factory bars and the zoo. Two metro stops or a tram from the centre, noticeably cheaper beds, and a rougher feel on the side streets after dark.
Check the metro line before you book
Two metro lines and a dense tram network make the outer districts genuinely viable: a 75-minute zone 1 ticket is 4.40 zł and 24 hours is 15 zł, so Wola, Ochota or Mokotów costs far less and adds ten minutes. Anything advertised as central but off both metro lines is usually a bus ride, not a walk.