Question

What areas in Pokémon Gold require Surf and/or Waterfall as further navigation?

Comments

By "accessible", do you mean the player can enter it or completely navigate it? Do places that are "accessible" with only one of cut or surf count? Do places that are "accessible" only with some other HM in addition to cut or surf count?

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Route 40 - Cianwood city
Dragon’s den
To get to red gyarados
All routes to cinnabar island
Fire gym in kanto

Hope this helped

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There's no way this answer is complete. I haven't ever played a Johto game, and I already know this is missing Newbark Town and whatever routes are between that and Kanto.

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Just Kanto things and Lugia stuff are missing I think.

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In most of the games I've played, about half the routes and caves have some sort of pond or beach on it. Is that not true for Johto?

Answer 1

"Areas" in this context is taken to mean any location within the game with a unique name. "Further navigation" in this context is taken to mean tiles that can be accessed legitimately, but not without Surf or Waterfall. If you wanted either of these to mean something else, you probably should've specified.

Johto
Blackthorn City
Cherrygrove City
Cianwood City
Dark Cave
Dragon's Den
Ecruteak City
Ilex Forest
Lake of Rage
Mt. Mortar
Mt. Silver
Mt. Silver Cave
New Bark Town
Olivine City
Route 28
Route 30
Route 31
Route 32
Route 34
Route 35
Route 40
Route 41
Route 42
Route 43
Route 44
Route 45
Slowpoke Well
Tohjo Falls
Union Cave
Violet City
Whirl Islands

Kanto
Celadon City
Cerulean City
Cinnabar Island
Fuchsia City
Pallet Town
Route 4
Route 6
Route 9
Route 10
Route 12
Route 13
Route 19
Route 20
Route 21
Route 22
Route 24
Route 25
Route 26
Route 27
Route 28
Tohjo Falls
Vermilion City

There are some locations, such as Viridian City, that can only be fully explored with Surf or another HM. As Surf/Waterfall aren't necessary in these places, they've been omitted.

Johto locations (Bulbapedia)
Kanto locations (Bulbapedia)