Hi
Have you thought about the Tissington Trail (
http://www.peakdistrict.gov.uk/__data/assets/pdf_file/0009/90486/hptisstrails.pdf)? If you drive to Parsley Hay just outside of Buxton where there's a great cafe and car park (
http://www.parsleyhay.co.uk/). You can choose how far you want to cycle: Toilets etc are all marked if you get a trail map from the bike shop and there's even cycle hire there. Can get busy in the Summer months.
Definitely recommend the Middlewood Way as per other posts. There's a good pub and cafe and picnic site stop near Nelson Pit Visitor centre - you could even start there:
http://www.stockport.gov.uk/2013/3000/8784/middlewoodwaymap?view=Standard
Another one I would recommend is the Sett Valley Trail from Hayfield to New Mills (
http://www.bikely.com/maps/bike-path/Sett-Valley-Trail-New-Mills-to-Hayfield-Derbyshire) - nice gentle one to start off with - playground on the way too! You are better off starting in Hayfield as there is a car park right at the start with toilets.
Finally Carsington Reservoir (
http://cycletrails.co/carsington.htm) (isn't bad, but gets REALLY busy at weekends in the Summer - not sure I'd recommend for a 4yr old as the trail is occasionally very narrow and does get steep in a few places. It's the other inconsiderate users you have to watch out for and there are lots of dog walkers too. You could start at Carsington Water Activity Centre and just cycle around there though as there's lots to do - shops, cafes, boat hire and just cycle the easier, wider bits either side of Carsington Water Activity Centre until he's a bit more weary of other users and able to brake easily and ride into a ditch/hedge to avoid a collision! WE tend to do a "reccy" ourselves before taking the children along so we know what we're up against.
This web site lists all the good ones that are nearby, most of which I've mentioned above:
http://www.peakdistrictinformation.com/outdoors/cycletrails.php
Hope this is helpful - we're now trying to find much longer routes that are still relatively safe from traffic and not too hilly now our children are 10,11 and 12. We did the Danube Cycle Way (Passau to Vienna) last Summer - definitely recommend to you when your son is a little older.
Hope all this is helpful.