Hi there,
I recommend getting a 7 day JR Pass here. The cost of the pass is about the same as a return ticket Tokyo - Kyoto using the Shinkansen. With the JR Pass you get 7 days of unlimited travel for the same price and any additional travel is basically what you save :)
I'd advise staying in Tokyo on the day when you arrive. The last train connection to Kyoto from Narita Airport with the JR Pass departs around 18:45 and you may not be in time in case your plane is delayed. Staying in Tokyo will be a much saver option and you can get some rest before traveling on.
For staying in Kyoto, you have two main options. One is to stay near Kyoto station. This is convenient as you don't have to carry your luggage far and you can get on the train easily.
You could also stay in the city centre near Kawaramachi/Shijou/Gion. Here is where you'll find the true admostphere and the experience will be more enjoyable but slightly less convenient, as there are no JR lines in the centre.
Hope this helps,
Daniel