Hobson's was a small ice cream shop in Santa Barbara, California that offered a new type of ice cream: blends. Yes, Hobson's was a pioneer for "pick your mix-ins," long before Cold Stone or the McFlurry's existed. A Japanese businessman decided that this unique style of ice cream, when marketed as a favorite of President Reagan (who was the Governor of California before ascending to the White House) would sell in Japan. Good call on his part. The flagship store in Nishi-Azabu has been there ever since, and while Hobson's Ice Cream is not in every town in Japan, there is one in every corner of the country.
The menu has expanded some since the 1980s to include crepes and specialty sundaes, but my favorite (and therefore, my recommendation) is the blended ice cream.
Just pick a flavor and your mix-ins (oreos, M&Ms, etc.), and whether you want a cup or a cone, and you're on your way to Treatsville.
If you're in Tokyo, perhaps you don't want to go completely out of your way for the ice cream, so allow me to make a more complete recommendation: start with dinner at Gonpachi (Nishi-Azabu) across the street--otherwise known as the "Kill Bill" restaurant because it served as the aesthetic inspiration for the set in Vol 1's final scene. After dinner, make your way over to Hobson's for dessert, and from there, you can access several of Tokyo's great nightlife spots, including Roppongi, Ebisu, and Shibuya.
If you're not in Tokyo, fret not--there are Hobson's all over Japan. Check out their website here for store locations.