Ok first of all..
"As you enter towards the 2-storey house..."
..is incorrect. You don't "enter towards". Entering and exiting already indicate a direction, so there is no need to add any further direction.
You would simply say:
"As you enter the 2-storey house..."
"Entering" is the action of going inside. As for the different between enter and entering - the latter is ongoing. Just how long does it take you to enter a house? If you literally just step through a door then nothing much is going to happen "while you are entering".
I don't think there are many cobblestone paths actually leading into houses, so I'm guessing you don't meant to say entering.
I think you mean to say:
"As you approach the 2-storey house there is a cobblestone pathway which makes your walk easier.
Before you enter the 2-storey house, there is a cobblestone pathway which makes your walk easier.
or, if there was some land around the house you could say:
As you enter the property there is a cobblestone pathway which makes your walk towards 2-storey house easier.
Lastly, you would normally say "cobblestone pathway", not "cobblestoned". It is a path made of cobblestone. You wouldn't say a "wooded door" or a "glassed window".
RE: your edit
Since my original answer you have re-written the following two sentences:
As you enter the 2-story house, there is a cobblestone pathway which makes your walk easier.
As previously stated I don't think the cobblestone pathway is "as you enter the house". The cobblestone path will likely stop before the door leading to the house. You walk along the cobblestone path as you approach the house.
While you approach the 2-story house, a cobblestone pathway before the house will make your walk easier.
Again, no. "While" is not correct here. You use "while" to show that two things are happening at the same time. For example "whistle while you work" - you can stop whistling and stop working, but the cobblestone path isn't an event that happens.