The sequence of locations in the Pokemon Blue/Red town map (if you just keep pressing the up button) is:
Pallet Town
Route 1
Viridian City
Route 2
Viridian Forest
Diglett's Cave
Pewter City
Route 3
Mt. Moon
...
43. Route 22
44. Route 23
45. Victory Road
46. Indigo Plateau
47. Power Plant
This entire sequence matches the order in which you encounter each of these areas in the normal course of gameplay, with the exception of Diglett's Cave, which you don't normally encounter until later in the game.
Is it possible to access Diglett's cave at an earlier point in the game, as is suggested by its location in the Town Map?