Well, everyone has their own idea of the best places, although some places stand out so much they absolutely should not be missed. For Kyoto, the typical Top 3 sites are Fushimi Inari, Kinkakuji, and Kiyomizudera, but there are so many other great places worthy of your attention.
You mention the Otagi Nenbutsuji Temple, which is not eerie at all - in fact it's one of the most whimsical places you'll ever see.
https://www.youtube.com/watch?v=efvtB_5jmjANow going to Fushimi Inari at 2 AM, that might be a bit eerie. And if you go to Otagi, the Adashino Nenbutsuji Temple is very close and worth a visit too.
https://www.youtube.com/watch?v=0PAE1Puv21YArashiyama Bamboo Forest is nice but you'll be through it in 20 minutes or so. Just bamboo in every direction. Tenryuji next to it is very nice though. The Iwatayama Monkey Park is not the best in the country, and requires a bit of a slog of a hill to reach, but it's a good break from just seeing temples/shrines, and it gives a good view over the city.
https://www.youtube.com/watch?v=MlAkO1gdZKgThe Togetsukyo Bridge is all but worth walking across and skipping. Historically it is famous and important, but today it's pretty much like any other bridge with cars and trucks roaring past. If you want to see a bridge, try Iwakuni or for modern, the Akashi Kaikyo Bridge.
A lot of the problem though is being one area - you can see a lot of places close together, or spend (and waste) a lot more time going from one part of the city to another to see what is "best". I should ask however if you have browsed this website on numerous good places in Kyoto:
http://www.japan-guide.com/e/e2158.htmlas well as seen the official Kyoto City tourism guide:
http://www.kyoto.travel/You'll find gems listed on both.
I can give a few often overlooked items you should consider.
The Jonangu Shrine which is southwest of Takeda Stn has some beautiful gardens and offers a relaxing experience without most of the crowds. The Murin-an Garden is a beautiful garden (located in between Nanzenji and Heian Shrine) that's nearly unknown to most including the tourist guidebook "experts". The Shugakuin Imperial Villa and Katsura Villa are also a feast for the eyes. And if you go to Fushimi Inari, close by are the Tofukuji Temple & Daigoji Temple which are worth seeing too, especially in for the autumn colors. Plus there are the Kamo Shrines, the Honganji Temples (which open around dawn and close to Kyoto Stn, so easy to fit is a schedule), and there are farther away places too like Kibune, Kurama, and Sanzenin. Of course, there are countless more I am not mentioning.
And since you didn't mention it yet, you absolutely should give at least half a day to see Nara. If you think that a temple is just a temple, you have not see the Todaiji - it will blow your mind and while other places might turn into a blue, this place you'll never forget for the rest of your life.
https://www.youtube.com/playlist?list=PL7LcPcmoSg-jGyApXWSTIKwkioxuAKw...I would suggest not to overdo the temples and shrines all in a row. I did that 35 years ago and by the end of the day, just about everything was a blur. I had trouble telling where I even took my photos. Break things up with some variety - the monkey park, the railway museum, the Nishiki Market, whatever. It'll keep things separate in your mind and you will overall enjoy your visit more.