Sorry its taken me a while to get this. Not sure how to time any of this. I have taken note of stations that you have not visited and tried to minimise revisits. Both routes some how end up in Harrow/Uxbridge areas...
Please correct me if any errors
ROUTE THAT COVERS MOST GROUND
1a.Take
District to Tower Hill. Walk to Tower Gateway and take
DLR to Limehouse. Take
C2C to West Ham and take
District to Upminster. Take
C2C fast back to Barking.
Take
London Overground to Blackhorse Road, change to
Victoria Line. Take service to Walthamstow Central, double back and go to Kings Cross St. Pancras. Take
Piccadilly Line Northbound to Cockfosters.
1b (Alternate, direct). Take Victoria Line Northbound to Kings Cross St. Pancras, change to
Piccadilly Line to Cockfosters.
2. At Cockfosters, take bus
384 (STOP B, start of route) to High Barnet. Take
Northern Line southbound to Camden Town (can change at Finchley Central to get to Mill Hill East, however the return train may leave you with a 15 min wait). Take Northbound
Northern Line to Edgware.
3. Take
BUS 142 (STOP F, towards Watford Junction) to Stanmore, and take
Jubilee Line Southbound.
If its getting late...
4a. Change at Wembley Park and take
Metropolitan Line Northbound to Harrow-on-the-Hill. Take
BUS 182 (or most buses from STOP A) to Harrow& Wealdstone, at this point, you can take Overground Northbound to Watford Junction (make sure your ticket is valid) and take
Southern/London Midland back to H&W or just take Bakerloo Line Southbound to London to end.
If you have a couple of hours to spare...
4b. As with a, but with additional stops. Take
Jubilee to Bakers Street, then Northbound Bakerloo to Harrow & Wealdstone (can pop up to Watford Junction if needed). Buses from stop M to Harrow-On-The-Hill. Take
Metropolitan to Uxbridge, then take
Piccadilly back to London to end.
ROUTE INCLUDING TRAMLINK & W&C LINE
Starting at Victoria Underground Station, take southbound
Victoria line to Stockwell (you can go to Brixton and double back to totally complete the line).
Northern Line to Morden.
Take
BUS 93 (STOP A toward Putney Bridge) to Wimbledon Station (you can take District and double back at Wimbeldon Park to finish that branch). Take
Tramlink to West Croydon. Change for
London Overground to Shadwell (can double back at Sydenham to cover Crystal Palace - New Cross could be done at another time, should you travel to Woolwich Arsenal or Lewisham on
DLR).
Take DLR to Bank and change for
Waterloo & City Line to Waterloo. Take
National Rail SWT to Richmond.
Take Northbound
District to Earls Court, then Westbound
Piccadilly to Heathrow.
a.
If you want to travel on Heathrow Express and Connect shuttles between terminals for free. Take Piccadilly to Terminal 5, change for Express service to Terminals 123, change again for Connect service to terminal 4. Take Piccadilly Line back towards Central London.
b.
If you dont want to travel on Heathrow Express and Connect. Take Piccadilly to Terminal 123 via 4, change for service to terminal 5 and then take Piccadilly back towards Central London.
Change at Acton Town for
North/Westbound Piccadilly service to Uxbridge. Double back to Ruislip and take Bus U10 to West Ruislip. Take
Central Line towards London (double back to Ealing Broadway (then NR to Paddington) from East Acton if wanted) to end.