Visit Rebbetzin Kolodetsky, go see R’ Aryeh Leib Steinman, R’ Chaim Kanievsky, and any other Rebbe or godol who is part of your mesorah. Do tunnel tours at Kosel Ma’aravi and see if you can see any other museums in the Jewish quarter – Keilim from the Beis HaMikdash, houses from the times of Bayis Sheini for example. Go to as many kevarim of tzaddikim that you can’t find in America – Tiveria, Amuka, Tzfas (there are erev R”Ch trips to the North to daaven at these places but I’m not sure how long you’ll be here).