How to make audio play only when the player is in a specific area?

You could check whether the character's torso is inside a bounding box delimited by two Vector3 values.

Another solution, especially useful if you plan on building complex shaped houses would be to have two invisible bricks serve as a "doors" and have a script inside both of them to listen for the "Part.Touched" event. If the inside brick is touched then the music triggers. If the outside brick is touched then the music stops. Note that the music would still persist for example if the player teleported out. Maybe combining the two solutions could solve this problem. I'll leave this to you as an exercise.

For the sake of simplicity, let's stick to the second solution.

Inside brick:

local player = game.Players.LocalPlayer
local character = player.Character

local part = script.Parent


local function onTouched(hit)
    if hit.Parent == character then
        -- I think having the sound in the local player's instance will
        -- only have it play for him but I am not entirely sure about this.
        local sound = player:FindFirstChild("Sound") or Instance.new("Sound", player)

        -- Replace the sound's assetId with that of your own music.
        sound.SoundId = "https://www.roblox.com/?id=138103237"
        sound.Looped = true

        -- If the character dies or resets then we stop the music as
        -- he respawns.
        character.onCharacterAdded:connect(function()
            sound:Stop()
            sound:Destroy()
        end)

        sound:Play()
    end
end


part.Touched:connect(onTouched)

Outside brick:

local player = game.Players.LocalPlayer
local character = player.Character

local part = script.Parent


local function onTouched(hit)
    if hit.Parent == character then
        local sound = player:FindFirstChild("Sound")

        -- We check if there was indeed a sound playing.
        if sound then
            sound:Stop()
            sound:Destroy()
        end
    end
end


part.Touched:connect(onTouched)