It depends what you're looking for of course, and I presume you are actually referring to both temples and shrines. The season really changes the atmosphere as well, and some places are especially good for the autumn colors. Others are good with the explosion of green in summertime. The cherry blossom and autumn leaf seasons are also wildly more crowded.
A few notable places:
The Honganji Temples & Shoseien Garden
These are some of the most impressive structures in Kyoto - yet often ignored by the crowds. They're also open around dawn, so they're easy to fit in if you can get up early. You can walk to them from Kyoto Station.
This shrine is mostly unknown to most, and has 5 varied and nice gardens. It's south of Kyoto Stn, and southwest of Takeda Stn.
This amazing place sits at the end of Arashiyama, so not so many find it. It's one of the most whimsical places you'll ever see in Japan.https://youtu.be/efvtB_5jmjA
Tucked away on Kyoto's east side in the mountains east of Shimogamo Jinja, this often overlooked place will amaze you if like the tanuki or Japanese raccoon-dog.http://www.tanukidani.com
Kyoto's most expensive temple which needs advance reservations (they pick the time) has what many regard as the best moss garden, which almost glows at you from late spring through autumn. It doesn't get 'crowded', since the number of visitors at any one time is tightly controlled. But if you can't sit in seiza or crosslegged for a long time for the prerequisite rituals first, maybe you should skip it.http://www.saihoji-kokedera.com
Very close to the Mt Hiei cable car, this place might have Kyoto's 2nd most expensive admission at 2000 yen. It's especially popular for its garden in autumn. That's when it gets crowded, but mostly by Japanese. Other times are much more tranquil.http://rurikoin.komyoji.com
This temple is about a 20 minute bus ride from the northern subway station Kokusai Kaikan. Some know it but it still doesn't get the big crowds like some other places. The moss garden from late spring is also wonderful - it also has gorgeous hydrangea. The garden is superb.http://www.sanzenin.or.jp
Not so many know Kyoto has its own Daibutsu or Great Buddha. This place is actually a temple and WW2 memorial. It's no Todaiji like in Nara, but nearly unknown and few visit it. It honors the dead from all sides.
Next to it is the Ryozen Gokoku Shrine and Museum of History, which focuses a lot on the fall of the Shogunate. The former has Sakamoto Ryoma's grave, but some may not like the imperial and wartime monuments + nihonjinron, a la Yasukuni in Tokyo. It's just south of Maruyama Park.http://www.ryozen-kwannon.or.jp/indexE.html
This is not a temple, but still one of Kyoto's most beautiful places. It's bypassed by those who just don't know it and shortchanged by those who do. It's the old home & garden of a prime minister at the end of the 19th century, and it's well worth your attention. It's in between Heian Shrine and the Nanzenji Temple.https://murin-an.jp
It also goes without saying that you can still visit the more popular places in the off hours and also avoid most of the crowds. Fushimi Inari is open 24/7, and you could have the place almost completely to yourself at dawn, and also pretty uncrowded in the evening.