We started for the City Palace - Kota Garh at 4pm after the heat subsided a bit. We did cut it close. Even though it worked out for us, I don't recommend it as entry to the palace is restricted after 5pm.
The entry fee was nominal. Rs. 100 per person for the Palace and Museum, and Rs. 50 for clicking pictures.
What I found fascinating about Kota was the section called Old Kota. This is the original area of the city built by the Kings of old. Although the roads are narrow and it is a bit more crowded, I was surprised to see that a vast majority of the city walls still stand tall. The gates and the walls for the most part have been well preserved and now are part of the heritage of the city.
Kota Garh is built on the banks of the river Chambal and the views from the palace are to die for. It is well maintained and also houses a museum that has paintings and murals depicting the stories of the city, an armory with weapons used a few centuries back; I didn't know that there was a weapon with was a cross between a sword and a pistol.