In Warsaw you can go to:"Umschlagplatz"
it's the spot where about 300,000 jews were deported to the death camps.
shul located at Ul. Twarda. Before the war there were many Shul Bulding's and additionally there were aprox 300 - 400 Shtiblach (where the chasidim Davened)
The Warsaw cemetery (Ul. Okopowa) where over 250,000 jews are buried including such greats as R' Chaim Brisker and the Netziv. The cemetery was only 1 of many, it was only opened in 1806. Warsaw was aprox. 40% jewish before the war.
Alot of jewish history is close by, such as ger which is about 1 hour away, Aushwitz 3.5 hours etc;
Taxis are cheap but try to know what the aproximate price should be before getting in to a cab because they can really rip you off. The aprox fare from the airport to city center, jewish area is about 35 - 40 zloty definitel never more than 50 with heavy traffic.