Tours from Xi'an that go to Hukou Waterfall will include this in the itinerary.
There is no high-speed train service (G- or D-series trains) to Yan'an. The closest cities with high-speed service are Xi'an and Taiyuan. Note that in Xi'an "regular" and high-speed trains use different stations, which means that transferring between a "regular" train from Yan'an and a high-speed train (e.g. to Guangzhou) would involve a fairly long subway ride.
Phoenix HillLantau Peak is located in Yanan city centre, Yanan is one of the four famous mountains. Lantau Peak's highest elevation 1132 meters, mountain range rover, overlooking the breathtaking views of the Yanan.
Yan'an NurseryA communist play that is part of the 2-day tours from Xi'an. In Chinese: 延安保育院. Usually costs extra and a bit like an opera yet if you do not understand Chinese you can forget about enjoying it.
Zaoyuan 枣园"Date Park" is a small public park that has the old housing of the Communist leaders. The part itself has not much to see but many souvenirs to buy.
Dog Head DatesCalled 狗头枣 as they are supposedly as big as a dog's head. These are healthy dates and one of the best places to buy them in China. You have to pay almost double in Beijing for example. People will let you try them from plates but be aware that this often means you are then led to a place to buy some. Better to just avoid the sellers unless you are prepared to buy from them.