How would I make my door so that you can only open it from a specific distance or less?

Here's a way you could do it using magnitude

local UIS = game:GetService("UserInputService")
local checkrange = 3
local player = game.Players.LocalPlayer 
local DoorOpen = false
UIS.InputBegan:Connect(function(key)

	if (player.Character:WaitForChild("HumanoidRootPart").Position - 		 
        workspace.Door.Position).Magnitude <= checkrange and key.KeyCode == Enum.KeyCode.E then
		if DoorOpen == false then
			DoorOpen = true
			--Open Door
		else
			DoorOpen = false
			--Close Door
		end
	end
end)

This checks if the player is at max 3 studs away from the door, and if they press the letter E. If they do, you then put in what you want the door to do.