Making a gui get displayed only at a certain distance?

How To Fix

A) After you make the table, you iterate through it using a generic for loop. Compare the mouse's target with values in the table.

B) Compare the magnitude of the difference in positions between the mouse's target and your character.

Efficiency Fixes

• You should use the Mouse.Move event, rather than firing every frame :)

local RunService = game:GetService("RunService")
local Player = game.Players.LocalPlayer
local Mouse = Player:GetMouse()
local ActiveParts = {"Door1","Door2"} --These are what activate the ui
local Tag = script.Parent
Tag.Text = "CLICK TO OPEN"

repeat wait() until plr.Character

local char = Player.Character
local root = char:WaitForChild("HumanoidRootPart")
local minimunDist = 16 --Minumun distance to activate ui

Mouse.Move:Connect(function()
    local Target = Mouse.Target
    local dist = (Target.CFrame.p - root.CFrame.p).magnitude --Get distance
    if dist <= minimumDist then --Check distance
        for _,v in next,ActiveParts do --Iterate through table
            if v == Target.Name then --Compare values
                Tag.Position = UDim2.new(
                    0,
                    Mouse.X-Tag.AbsoluteSize.X,
                    0,
                    Mouse.Y-Tag.AbsoluteSize.Y
                )
                Tag.Size = UDim2.new(0.1,Tag.TextBounds.X,0,25) 
                Tag.Visible = true
            else
                Tag.Visible = false
            end
        end
    end
end)

This script works but it only has one problem, the range won't chance as you move. If you can fix that you will be good to go.

This is how you should place stuff:

StarterGui - Imgur

Workspace - Imgur

This is the VariableHandler:

--[[
    This script won't work if players decide to be R15 or not
--]]

local player = game:GetService("Players").LocalPlayer
local char = player.Character
local torso = char.Torso  -- change char.Torso to char.UpperTorso if the game is R15
local ActiveParts = workspace:WaitForChild("Door1")
local WALL = ActiveParts.wall
_G.WALLrange = (torso.Position - WALL.Position).magnitude

and this is the TextHandler:

local RunService = game:GetService("RunService")

local player = game:GetService("Players").LocalPlayer
local char = player.Character
local torso = char.Torso
local hum = char.Humanoid
local mouse = player:GetMouse()

local ActiveParts = workspace:WaitForChild("Door1")

local interface_magnitude = 6.5

local Tag = script.Parent
Tag.Text = "CLICK TO OPEN"

Tag.Visible = false

RunService.RenderStepped:connect(function()
    local tpos = torso.Position
    local Target = mouse.Target -- Get the object the mouse is hovering over    
     if Target and ActiveParts:IsAncestorOf(Target) then
        if _G.WALLrange >= interface_magnitude then

            Tag.Size = UDim2.new(0.1,Tag.TextBounds.X,0,25) 
        Tag.Visible = true

        -- If no target exists, then...
        else

        -- Hide the tag
        Tag.Visible = false 

        end
        end
    -- Update the tag's position with the mouse
        Tag.Position = UDim2.new(0,mouse.X-Tag.AbsoluteSize.X,0,mouse.Y-Tag.AbsoluteSize.Y)
        end)