Here are some photos of the places we visited on a three-day trip to neighboring Shănxī (陕西) province (spelled Shaanxi in pinyin, to distinguish it from Shānxī 山西 province).
The road from Hánchéng (韩城) to Yíchuān (宜川)
Húkŏu Pùbù waterfall (壶口瀑布)
Xī'ān (西安), Small Wild Goose Pagoda & City Museum
Xi'an 西安 - Hancheng 韩城
Regular buses from bus station opposite the train station.61 yuan, 3 hours.
Hancheng 韩城 - Dangjiacun 党家村
Taxi 20 yuan, 20 mins
Entry ticket: 30 yuan
Accommodation: 10 yuan per person
Hancheng 韩城 - Yichuan 宜川 (for Hukou Waterfall 壶口瀑布)
Departed from the old bus station 06:30 and 11:30, 30 yuan, 4.5 hours
In hindsight, we should have waited by the side of the main road, at the turnoff to Dangjiacun, rather than go all the way back to Hancheng at 6am. The Yichuan bus went right past at about 6.45am.
Yichuan 宜川 - Hukou Waterfall 壶口瀑布
The bus driver on the Hancheng-Yichuan bus arranged a driver to meet us for the trip to the waterfall. Two of us paid 220 yuan, including the drive there and back, and our entrance tickets (price 80 yuan per person). He had some understanding with the gate people, and was able to take us in for the cost of one ticket. He pocketed the difference, and we got a driver for 60 yuan (total distance 100 km). We entered on the Shanxi side of the river. We paid an extra 21 yuan per person to go down a spiral staircase into a cave, which lets you see the waterfall at the base of the falls.
Yichuan 宜川 - Xi'an 西安 (east bus station)
Last (sleeper) bus 17.3085 yuan, 6 hours
We got the last two lower-berth tickets at 14:30, and apparently the bus was sold out by 15:00 (we know, because they sold 'floor' tickets, and we ended up with someone on the floor between us, who said she was unable to buy a regular ticket at 15:00). So, although it wasn't a problem for us, it might have been better to buy the Xi'an tickets before heading to the waterfall. In any case, Hancheng-Hukou-Xi'an is very possible in a day, if you don't mind the long bus distances: We woke up in Dangjiacun at 05:00, and arrived into Xi'an at 23:00.