A few planetariums in Tokyo have seats where you lie flat instead of sitting up, so the stars projected on the dome fill your whole view. Only a handful of these seats are offered per show, so reserve one together with your ticket. Most shows are narrated in Japanese, but some offer English audio, and the music and the stars need no translation.
At the front of the dome are two kinds of special seats: a round, cushioned "cloud seat" and a flat "lawn seat" of soft artificial grass, where you lie back and watch the night sky overhead. Only a few of each are offered per show, so book one in advance. The planetarium is on the rooftop of Sunshine City in Ikebukuro, and free English audio guides are available for some shows.
Crescent-moon-shaped seats at the front of the dome let you lie back and take in the whole sky above you. There are only three per show, so reserve one when you book your ticket. The planetarium is inside Tokyo Skytree Town, close to Oshiage Station, and a few shows offer English audio.