Best to stay near Central Kyoto or Kyoto station?

Kyoto station is a bit far from the nice Gion area that has most of the restaurants and bars. It's best to stay around there and it's pretty central too. There are a lot of restaurants in small alleys and by the water and the Nishiki Market is pretty fun to walk. 

Visit Kiyomizu-Dera, specially during sunset it's a nice place to see. 

Kyoto is small enough that it won't make a huge difference either way, in my opinion. Yes, Gion is neat and more historic, but the station itself and the area around it has plenty going on, too. You will undoubtedly  find yourself in both areas, and they're about a 5 to 10 minute train ride or taxi ride apart. 

Although i do agree that Gion is the most interesting area in kyoto, i did stay at the Hotel Granvia (that's hotel granvia at the train station) and didn't think it was very far, also you can find plenty of restaurants around for an amazing kaiseki experience. but definitely check out the market as well, and of course climb the hill through the arches of Fushimi Inari Taisha to the most serene place on earth.

I spent a week in Kyoto and can second Joanna Riquett suggestion, head to the Gion area.

Both Kyoto Station and Downtown Kyoto in Central Kyoto are highly convenient for public transportation. The main difference between the two is that Kyoto Station is a transportation hub and all public transportation is under one roof; while for Downtown Kyoto, the public transportation (i.e. bus, subway) is a bit scattered but this shouldn't be a problem since the Downtown area is kind of compact. 

If you have stroller, I would suggest you to avoid taking buses as these are usually crowded even during non peak season.

Personally, I would prefer to stay in Downtown Kyoto since it's just 10-15 minutes walk to Gion Shijo Station (the historical part of town) while still having immediate access to shopping, nightlife and affordable restaurants. The Downtown area is pedestrian friendly too!

Hope this helps.

Tiffy :)