Firstly I'm going to start off by saying, I don't think that you can really count the City in the Sky area as a province, after all it as its title states, it is a city.
Back on topic, My favourite province is the Lanayru Province, The scenary there is beautiful. The area has a lot to do and looks awesome when you look on the Lake from above. It is also home to the Zora's Domain and the river leading down from there if I remembe correctly, This area as a whole is just perfect. Although it is however, not home to my favourite race who are based on Death Mountain of the Eldin Province, The Zora's still give you some great help and a useful tunic.
Morpheel also stationed here in one of the best temples in the games to be fair although I didn't like it that much compared to several others. Morpheel was a fun boss battle though.