Cake

The most popular cake in Japan is probably ショートケーキ (shortcake), which is a type of layer cake. Usually a strawberry on top and in one of the layer with cream.

A good site to check how certain cakes look like or call at pâtisserie is here:

http://lesanneesfolles.jp/gateaux/

(my goto when I live in Ebisu)

Classic Cakes

ショートケーキ

Wiki

Shortcake

キリッシュトルテ

Wiki

Kirsch Torte

モンブラン

Wiki

Mont Blanc aux marrons

A good one in Kyoto: http://www.malebranche.co.jp/montblanc/

Places

ケーキ屋
Any place sells cake.

パティスリー
A place sells cake and bakery. Originated from France and Belgium. The chef need to pass sort of certifications.