I spent a month there as part of a three month East Asia trip.
Transport is great so no real need to pick an area. In two weeks I'd spend a couple of days in Nikko as it gets you out of the cities.
Koyoto arrive everyway as early as possible.Kiyomizu-dera opens at 6am be there then and you can do that and the area around it before the tours arrive.Fushimi Inari Taishaarrive at dusk and walk up taking a path to the right through the bamboo forest ( it's better than the more famous one) You get to the top in the dark. More atmospheric and lots less tourists. Carry on the walk down for a fantastic overview of the city.
Other famous places go later.There is plenty to see in-between time that isn't on the over tourism route.
So many templates and so much up hill walking
Tokyo the new TeamLab at Azabudai Hills is impressive but get the tickets now.
Off the beaten track I'd advise local restaurants are great join the queue or put your name down on the door. Local temples are just as impressive as the famous ones.
Go to the bar at the Asahi building (can't miss the golden turd on it) just before sunset for a drink and amazing view. You will have to wait for a table but it moves quite quickly
If you have to drop somewhere drop Osaka.
As for practical tips get a SIM card at the airport, get a Saica card at the airport. Understand the different train companies and take the local bus to get around. Someone will try and help you always.