The karst hills in both photos are from areas near Guilin. The city itself is charming by Chinese standards, but it's not spectacularly scenic as one would have fancied. Instead, you would need to go outside of the city, at least to a town called Yangshuo. Very popular with both Chinese and Westerners, it's a great place to rent a bike and just ride around the countryside. A littler farther from Yangshuo is Xingping, a smaller, more charming town that's arguably the better place to view the karst hills via the bamboo raft on Lijiang (Li River, not Lijiang, the town, in Yunnan province). Near Xingping's boat dock is the location depicted on the 20RMB bill. There are also good hiking opportunities in Xingping.

If you devote 4-7 days, you can fly into KWL and experience all 3 of Guilin, Yangshuo, and Xingping. My personal experience: I went directly to Xingping first (KWL airport into Guilin city, bus to Yangshuo, and then a rickety bus to Xingping). Oneway bamboo raft up the Li River, and then hike back into town (iirc, there is also a tram that travels at least part of the way along the river). In Yangshuo, there are lots more outdoor activities that can be arranged (rock climbing, paragliding, etc.). Rental bikes are everywhere for $2/day (and that was probably on the expensive side). Cormorant fishing is actually now an evening performance. I don't know exactly where it takes place, but you can arrange it from your hotel in either Yangshuo or Xingping.
Safe travels!

Xingping, Guangxi