I grew up in London, definitely a city without any kind of grid system. I lived in Oxford. No grid. I moved to Leeds. No grid. Later I moved to Truro in Cornwall. Definitely no grid. Now I live in Falmouth - guess what? Yup, no grid.

Conversely, any time I'm in a town or city with a grid system, I can't find my way around. I'm not used to cities where north-south roads are letters and west-east roads are numbers. I can't cope with that sort of logic and it hurts my brain.

In order to navigate in a normal (as opposed to a grid-city) you have to pay attention to what you're passing and look out for landmarks and also count them. Whenever you go through an intersection you need to turn around and look carefully at what you see - so you'll know the landmark when you're coming back the other way. Find weird stuff to look at - a fish emerging from a roof (Camden, London) or a well-endowed statue banging a drum (Truro, Cornwall). You count the landmarks as you go past and of course you count them backwards when you return.

Nowadays you can always check your GPS, sadly.

Good luck!