Center of TokyoTokyo station is next to the Imperial Palace. It's the hub of Tokyo's shinkansen (bullet train) system that connects Tokyo to the rest of Japan. Tokyo station (along with the Imperial Palace) is the center of Tokyo.
The neighbourhoods directly surrounding the Imperial Palace are Tokyo's oldest neighbourhoods. These include Jinbocho, Otemachi, Marunouchi, Ginza, Toranomon, Nagatacho and Kudanshita.
Downtown TokyoTokyo people speak of Tokyo's geography in terms of train lines.
There's a loop line around central Tokyo called the Yamanote line. The neighbourhoods on this line (and neighbourhoods within the loop) are all considered downtown Tokyo. This makes Tokyo's downtown massive: the loop is 34.5 kilometers (21.4 miles) around.
Uptown TokyoThe Yamanote loop includes five stations that serve as Tokyo's main connecting hubs: Shinjuku, Ikebukuro, Tokyo, Shibuya, Shinagawa and Ueno stations.
Anything outside the Yamanote loop is considered uptown or suburbia. Neighborhoods that connect directly to the loop by a 20 minute ride (or less) are uptown. For example, Kichijoji is 20 minutes from Shibuya by Inokashira Line. Therefore, Kichijoji is uptown.
Tachikawa is 45 minutes from Shinjuku. Therefore, Tachikawa is suburbia.
Greater TokyoTokyo is surrounded by three massive areas (that are essentially suburbs of Tokyo): Chiba prefecture, Saitama prefecture and Kanagawa prefecture (Yokohama). These also link into central Tokyo by train (they're as close as 20 minutes to the loop).
Tokyo MapThe following map shows how various train lines link into the the Yamanote line (the green loop in the center). Keep in mind — this map only shows the train lines of one company (Japan Rail East). There are 30 train companies in Tokyo. It's far to complex to put all train lines (121 of them) and stations (882 of them) on a single map.
credit: JR East