Mornington Crescent, 3328 bytes

Take Northern Line to Leicester Square
Take Piccadilly Line to Heathrow Terminals 1, 2, 3
Take Piccadilly Line to Holborn
Take Central Line to Holborn
Take Central Line to Bank 
Take District Line to Hammersmith
Take District Line to Gunnersbury 
Take District Line to Hammersmith
Take District Line to Parsons Green 
Take District Line to Bank 
Take District Line to Hammersmith
Take District Line to Bow Road 
Take District Line to Hammersmith
Take District Line to Upminster
Take District Line to Hammersmith
Take District Line to Parsons Green 
Take District Line to Parsons Green 
Take District Line to Gunnersbury
Take District Line to Paddington 
Take District Line to Hammersmith
Take District Line to Parsons Green
Take District Line to Bank
Take District Line to Hammersmith
Take District Line to Gunnersbury
Take District Line to Barking 
Take District Line to Acton Town
Take Piccadilly Line to Holloway Road
Take Piccadilly Line to Acton Town
Take District Line to Acton Town
Take District Line to Gunnersbury 
Take District Line to Hammersmith
Take District Line to Parsons Green 
Take District Line to Elm Park 
Take District Line to Acton Town
Take Piccadilly Line to Heathrow Terminal 5
Take Piccadilly Line to Acton Town
Take District Line to Acton Town
Take District Line to Parsons Green 
Take District Line to Bank
Take District Line to Hammersmith
Take District Line to Plaistow 
Take District Line to Hammersmith
Take District Line to Gunnersbury 
Take District Line to Mile End 
Take District Line to Elm Park
Take District Line to Mile End
Take District Line to Paddington
Take Circle Line to Paddington
Take Hammersmith & City Line to Barking
Take Hammersmith & City Line to Paddington
Take Circle Line to Paddington 
Take Bakerloo Line to Piccadilly Circus
Take Bakerloo Line to Piccadilly Circus
Take Piccadilly Line to Turnpike Lane
Take Piccadilly Line to Turnpike Lane
Take Piccadilly Line to Leicester Square
Take Piccadilly Line to Leicester Square
Take Northern Line to Charing Cross
Take Northern Line to Charing Cross 
Take Northern Line to Embankment
Take Circle Line to Embankment
Take District Line to Upminster 
Take District Line to Embankment
Take Circle Line to Embankment
Take Northern Line to Charing Cross 
Take Northern Line to Embankment
Take Circle Line to Westminster
Take District Line to Gunnersbury 
Take District Line to Bow Road
Take District Line to Bank
Take District Line to Hammersmith
Take District Line to Gunnersbury
Take District Line to Paddington
Take Circle Line to Paddington
Take Circle Line to Moorgate
Take Metropolitan Line to Chorleywood
Take Metropolitan Line to Moorgate
Take Circle Line to Moorgate
Take Circle Line to Bank
Take District Line to Bow Road
Take District Line to Hammersmith
Take District Line to Gunnersbury
Take District Line to Plaistow
Take District Line to Gunnersbury
Take District Line to Mile End 
Take Hammersmith & City Line to Paddington
Take Circle Line to Paddington
Take Circle Line to Hammersmith
Take District Line to Mile End
Take District Line to Bow Road
Take District Line to Mile End
Take Hammersmith & City Line to Paddington
Take Circle Line to Paddington
Take Bakerloo Line to Charing Cross
Take Bakerloo Line to Paddington
Take Circle Line to Bank
Take Circle Line to Bank
Take Northern Line to Mornington Crescent

Try it online!

I thought I could easily outgolf the existing Mornington Crescent answer by dozens of stations, but in the end its only 240 bytes shorter.

Short explanation: I extract following strings:

Heathrow Terminals 1, 2, 3 (also extracting the numbers for some operations)
--                     --

Holloway Road
  ---

Westminster
-

Chorleywood
  ---     -

The strings are cut in pieces, using the left and right substring functions of Gunnersbury and Mile End with the integers of "Heathrow Terminals 1, 2, 3" and "Heathrow Terminal 5" (which can be extracted using Parsons Green).

Then I concatenate them in Paddington and append a "!" by using the char code of (space)+1.

Source:

// ### Milestone: Extract "He", 1, 2, ", " from "Heathrow Terminals 1, 2, 3"

// Get "Heathrow Terminals 1, 2, 3"
Take Northern Line to Leicester Square
Take Piccadilly Line to Heathrow Terminals 1, 2, 3

// Copy that string
Take Piccadilly Line to Holborn
Take Central Line to Holborn
Take Central Line to Bank // Hammersmith = "Heathrow Terminals 1, 2, 3"

// Prepare for left substring
Take District Line to Hammersmith
Take District Line to Gunnersbury // Gunnersbury = "Heathrow Terminals 1, 2, 3"

// Extract 1 from "Heathrow Terminals 1, 2, 3"
Take District Line to Hammersmith
Take District Line to Parsons Green // Acc = 1, Parsons Green = ", 2, 3"

// Copy and store it somewhere (Parsons Green only returns its stored value if it gets a number)
Take District Line to Bank // Hammersmith = 1
Take District Line to Hammersmith
Take District Line to Bow Road // Bow Road = 1

// Store it in Upminster for later calculations
Take District Line to Hammersmith
Take District Line to Upminster

// Store 2
Take District Line to Hammersmith
Take District Line to Parsons Green // Acc = ", 2, 3"
Take District Line to Parsons Green // Acc = 2, Parsons Green = ", 3"

// Get "He"
Take District Line to Gunnersbury

// Store it in Paddington for concatenation
Take District Line to Paddington // Paddington = "He"

// Extract ", " from ", 3"
Take District Line to Hammersmith
Take District Line to Parsons Green
Take District Line to Bank
Take District Line to Hammersmith
Take District Line to Gunnersbury // 2 was still stored in Gunnersbury

// Store it somewhere
Take District Line to Barking // Barking = ", "

// ### Milestone: Extract "llo" from "Holloway Road"

// Get "Holloway Road"
Take District Line to Acton Town
Take Piccadilly Line to Holloway Road

// Prepare for left substring
Take Piccadilly Line to Acton Town
Take District Line to Acton Town
Take District Line to Gunnersbury // Gunnersbury = "Holloway Road"

// Store 3
Take District Line to Hammersmith
Take District Line to Parsons Green // Acc = 3
Take District Line to Elm Park // Elm Park = 3

// Get 5 from "Heathrow Terminal 5"
Take District Line to Acton Town
Take Piccadilly Line to Heathrow Terminal 5
Take Piccadilly Line to Acton Town
Take District Line to Acton Town
Take District Line to Parsons Green // Acc = 5

// Copy and Store it somewhere
Take District Line to Bank
Take District Line to Hammersmith
Take District Line to Plaistow // Plaistow = 5

// Get "Hollo" from "Holloway Road"
Take District Line to Hammersmith
Take District Line to Gunnersbury // Gunnersbury = 5

// Prepare for right substring
Take District Line to Mile End // Mile End = "Hollo"

// Get "llo" from "Hollo"
Take District Line to Elm Park
Take District Line to Mile End

// Append it to "He"
Take District Line to Paddington
Take Circle Line to Paddington

// Append ", "
Take Hammersmith & City Line to Barking
Take Hammersmith & City Line to Paddington
Take Circle Line to Paddington // Paddington = "Hello, ", Acc = ", Hello, "

// ### Milestone: Get "!" by adding 1 to char value of " "
// Reverse acc
Take Bakerloo Line to Piccadilly Circus
Take Bakerloo Line to Piccadilly Circus
Take Piccadilly Line to Turnpike Lane
Take Piccadilly Line to Turnpike Lane

// Get ASCII value of " "
Take Piccadilly Line to Leicester Square
Take Piccadilly Line to Leicester Square
Take Northern Line to Charing Cross
Take Northern Line to Charing Cross // Acc = 32

// Add 1
Take Northern Line to Embankment
Take Circle Line to Embankment
Take District Line to Upminster // 1 was stored in Upminster earlier
Take District Line to Embankment
Take Circle Line to Embankment
Take Northern Line to Charing Cross // Charing Cross = 33

// ### Milestone: Append "W" from "Westminster"
// Get "Westminster"
Take Northern Line to Embankment
Take Circle Line to Westminster

// Get "W"
Take District Line to Gunnersbury // Gunnersbury = "Westminster"
Take District Line to Bow Road
Take District Line to Bank
Take District Line to Hammersmith
Take District Line to Gunnersbury

// Append it to "Hello, "
Take District Line to Paddington
Take Circle Line to Paddington

// ### Milestone: Append "orl" and "d" from "Chorleywood"
// Get "Chorleywood"
Take Circle Line to Moorgate
Take Metropolitan Line to Chorleywood

// Save it for copy
Take Metropolitan Line to Moorgate
Take Circle Line to Moorgate
Take Circle Line to Bank

// Bank had 1 in it, so save it for later
Take District Line to Bow Road

// prepare left substring
Take District Line to Hammersmith
Take District Line to Gunnersbury

// get "Chorl"
Take District Line to Plaistow
Take District Line to Gunnersbury

// get "orl"
Take District Line to Mile End // 3 is still stored in Mile End

// append it to "Hello, W"
Take Hammersmith & City Line to Paddington
Take Circle Line to Paddington

// get "d"
Take Circle Line to Hammersmith
Take District Line to Mile End
Take District Line to Bow Road
Take District Line to Mile End

// append it to "Hello, Worl"
Take Hammersmith & City Line to Paddington
Take Circle Line to Paddington

// get "!" and append it to "Hello, World"
Take Bakerloo Line to Charing Cross
Take Bakerloo Line to Paddington

// go home
Take Circle Line to Bank
Take Circle Line to Bank
Take Northern Line to Mornington Crescent