General Advice for Kyoto
Don't try to see more than 3-4 temples in one day, unless you're a huge temple/history buff. You will get temple burnout for the rest of your trip. To the average tourist, the temples don't look much different after you've seen a few. If you must, make sure to stagger different types of temples (Buddhist and Shinto).
Arrival at Kyoto station
We arrived to Kyoto station around 10am. It was still pretty early, so it wasn't check-in time for our AirBnB yet. We stored our luggage at Kyoto Station (there are a number of different luggage storage options there, just google "Kyoto Station luggage storage") so we could come back for it later and do some sightseeing first.
We took the JR Nara line from JR Kyoto station to Fushimi Inari Taisha, which is one of my favourite shrines in Japan. This is the shrine with the iconic red/orange torii gate path up the mountain that is often shown on anything Japan-related. It's generally pretty busy, and if you want a photo with no people, you ought to be here by 5 or 6am in the summer. Fushimi Inari is open 24/7.
Some other places to visit
Note: Kyoto can be split up into North, East, South, and West Kyoto. Fushimi Inari is all the way in the south. I'm going to list all the places of note I've been in Kyoto here. I've been to more than these but some of them weren't very noteworthy, or I went for specific events like to view fall foliage at certain temples and wouldn't be applicable to a general itinerary.
Kiyomizu-dera: Located to the west area of Kyoto and doable with Fushimi Inari Taisha in one day. Buddhist temple with a fantastic shopping street. In my opinion, a must-visit for anyone visiting Kyoto for the first time. The shopping street is just as impressive as the temple itself. If you visit some of the back alleys, there are some pottery stores for those interested.
Kinkaku-ji: Somewhat of a controversial opinion, but I personally don't believe Kinkakuji is worth a trip to. It's located pretty far out to the northwest of Kyoto, far from most other destinations. Is it a pretty temple? Yes. How long would you spend there? 15 minutes, probably, maybe longer depending on how many people you have to fight to get a pretty photo. Google "Kinkakuji" and you see how those photos all look alike? That's because the photo you'll get when you're there is going to look exactly like that. Unless you had a lot of time in Kyoto, I would recommend saving it for somewhere else instead.
Kawaramachi Street: One of the most bustling areas of Kyoto. It's pretty hard to miss, since so many train stations have stops here (Kyoto-Kawaramachi station, Gion-Shijo station, etc). There are a number of big department stores here too (Takashimaya, Tokyo Marui) as well as lots of stores selling traditional Kyoto crafts and sweets. There are also a ton of restaurants to choose from here too, and I generally take friends or family to have dinner here when we're in Kyoto.
Gion: You might know this as the area where you have a chance of bumping into geishas. Good luck, since I've been there many times and I saw one! It's a really nice little area though, and it's probably a lot smaller than you would expect. Worth taking a look, it won't take you much time. Think of it as an after-meal stroll after Kawaramachi.
We stayed at an AirBnB not too far from Kyoto station, just a few bus stops away. We had a lot of luggage though, so we took a taxi instead.
Arashiyama day trip
We headed to Arashiyama, located all the way to the western side of Kyoto. Arashiyama is known for the bamboo groves and a mountain with monkeys that you can feed. There's also a very touristy shopping street. Arashiyama is not only full of foreign tourists but it's also very popular amongst domestic Japanese tourists as well.
The monkey mountain is a little bit of a hike, but if you do it at your own pace then it shouldn't be a problem for most people. If you're short on time, do not run up the mountain just to see the monkeys just to run down after 5 minutes of feeding the monkeys. Unless you're very fit I suppose, unlike me.