Kyoto is beautiful, ancient, and full of more things than you possibly can do in a week. If you’re visiting, you must prioritize. Make a must-see list, and also a like-to-see list. Leave time for people watching, soaking in the city’s ambiance, and bad weather. And don’t worry about seeing it all. There are dozens of famous temples scattered around. You will miss some of them, but as long as you’ve experienced Kyoto, as a city, there’s no reason to rush to check boxes off a list.
More practically: unlike Tokyo, which runs on the trains, Kyoto is about buses and subways. Look into passes for those.
There are tons of places to stay in the city. Hostels are reasonably priced. But if you have a little more padding in your budget, a traditional ryokan is an experience worth having. If sleeping on the floor doesn’t strike your fancy, the Sakara Hotel is a great blend of Western and Japanese styles. I thoroughly enjoyed my stay there.
Finally, bring good walking shoes and an umbrella. Armed with these and a map, the city is yours.