Why didn't the Mongols make Baghdad, Kiev, and other various cities that they conquered that were large and rich their capital? Did the Mongols just have an aversion towards large palaces, temples, and monuments?
I'll take a shot answering this question about one of the most interesting empires of the history. My knowledge is all from research about the Mongols by interest
As you might know, the Mongols were nomadic people living in the Eurasian Steppe. Before Genghis Khan united the rivaling tribes in the Mongolian regions, they were living in typical mobile Mongolian tents known as Yurts.
What you also have to have to be aware of is that the incredible rise of the Mongol Empire happened exceptionally fast and the transition from Yurts to cities that you mention was not yet possible during the time Genghis lived as yurts were deeply rooted in Mongolian culture and history. It's also said that Genghis khan expressed disgust towards enormous cities because it made the population lazy which later on was proved by conquering them. The yurts played an important beneficial role in being able to crush his enemies who often were surprised by how fast his army could move and keeping their families nearby in yurts which takes between 30 min to 3 hours to set up. Genghis Khan himself lived in an enormous yurt pulled by 22 oxen commanding his entire empire from it. An example of Genghis Khans excellent use of Yurt is during the invasion of the Jin empire by bringing with him most of the population of his empire to the doorstep of the Jin empire with a large gathering of families in the yurts located safely but in reach of the outnumbered Mongolian army.
The Mongol empire got it's first city just like any other empire at that time. It was Gengis Khan's son Ögedei who built walls and enlarged the city of Karakorum where he centralized the governance of the Mongolian empire. The city itself didn't last that long as the center of the Empire as Kublai Khan established the Yuan Dynasty in China having Khanbaliq (Beijing) as the capital. And at that time, the Mongol empire wasn't only divided into two khanates but four khanates over several continents.
Edits: Grammar and spelling errors