You trade a Pokemon to your game that already knows cut to avoid going to the S.S. Anne all together. Then later when you get Surf go to the S.S. Anne and then surf to the right You can't get Mew from it though.
Go east from cerulean city keep going until you reach water go south and into the cave this is Rock Tunnel.
Head back to Cerulean City and go east then use Cut and follow the path all the way to Rock Tunnel pass through the tunnel to reach Lavendar Town then go west and go in the underground path go through here then go west to reach Celadon City where your next badge is.
The Cerulean Cave is in Cerulean City. You have to surf from a place around Cerulean Cape down to the Cerulean Cave. The Cerulean Cape is north of Cerulean City across the bridge.Go to the north end of the nugget bridge then left down the grass and follow the mountain to it. Btw you'll need flash and you can find Mewtwo in it.
Celadon City is southwest of Cerulean City, west of Saffron City and north of Fuschia City. In the map I've linked you to below, Celadon is number 1. http://pokedream.com/games/fireleaf/worldmap/worldmap.png You cannot reach Celadon through Saffron at first as guards block the way. However, by taking the underground walkway from west of Lavender, you can take a shortcut to Celadon.
Just go to the right (east) of Cerulean city. You will go past the Rock tunnel and see a water way. Surf down the water way and it will lead you right to the power plant. (the power plant is also a green dot on your poke gear map).
Go east from cerulean city keep going until you reach water go south and into the cave this is Rock Tunnel.
Head back to Cerulean City and go east then use Cut and follow the path all the way to Rock Tunnel pass through the tunnel to reach Lavendar Town then go west and go in the underground path go through here then go west to reach Celadon City where your next badge is.
Go back to Cerulean City then go east use Cut to get past the tree and keep going east until you reach Rock Tunnel this leads you to Lavendar Town go west from there to reach Celadon City where your 4th gym is.
It's located nearby Cerulean City to reach there go to route 24 use Surf then follow the water down until you reach the cave.
Simply follow route 10 until you reach a Pokemon center with a bunch of cuttable trees near it. It's east of Cerulean city if you look at your map. The entrance to the cave is to the left of the Pokemon center.
North of Cerulean city.
The Cerulean Cave is located in the west part of Cerulean City. If you head north, you will notice a water way to the left of the bridge. Surf on that waterway and you will eventually reach Cerulean Cave.
After Vermilion City will be Celadon City and to reach there first you must use Cut on a tree east from the Cerulean City gym to continue on a route which leads to Rock Tunnel. You must pass through Rock Tunnel and then you will reach another route if you go south from there you will reach Lavendar Town and from there you must go west to another route which has an underground path at the far end go inside there. Go through the path and you will reach the other side of the route you were on previously now just head a little bit up and then left to reach Celadon City.
Yes, it does. Remember that you can only see an object because of the light from it that travels towards you. You can see up a tunnel when you are standing at the bottom of it, which means that light can reach you. Of course, you may not be able to see the light from an object if something is blocking it. You won't be able to see the entire tunnel because the slope will mean that part of the light from the upper part of the tunnel will be blocked by the roof.
The "tunnel" that magma travels through is called a vent.
Its south of cerulean city jump down the ledges to reach it.
After getting the 3rd badge you need to do the following: Go to cerulean city then head east and cut the tree and keep heading east until you reach rock tunnel, Go through rock tunnel, enter lavendar town and then head west from there and eventually you will find an underground path nearby, go in and after you go through it go west and your in celadon city.