Not what I class as “decent” riding , but if you get up early enough you could go for a pootle around Hampstead Heath.The dog would probably show you the way.
Cycling is prohibited for the most part & the parks police
love to chat to cyclists who stray from the cycle route. 😕
Go and have a look up by Spaniards road , Sandy Heath , Kenwood & follow your nose- (permitted cyclepath up to Spaniards)
I’ve not been for a while to be honest, some of the locals are either too friendly(especially North wood!) or not at all.If you know what I mean. 😉
Alternatively, for better riding, Cockfosters tube and go for a play around Trent Park and then maybe cross the A111 to Monken Hadley Common.
Never done the dog & a bike thing so not sure where you can take them both on public transport.- Epping could be good or go to Hertford and explore Broxbourne(better than Epping).Take a compass & mud tyres 🙂