I still don't use a Sat Nav* although do look up location before I leave if I'm not familiar with the town (had a driving job in my youth, and only ever holidayed in UK so have walked/cycled trained travelled/driven to visit most towns and cities in the UK).
However a simple rule of thumb is that city /town centre places have older road names eg 'Street' 'Lane' or 'Road' . You can then pick up other clues as to location If you look around the town you are heading to chances are the roads to the nearest towns will be labelled accordingly eg for on any town along A4 , Bath Road heads west to Bath, London Road will be the opposite direction. Likewise 'West' 'East' will be to left side of town centre and right respectively, likewise the more modern sounding 'Southern Road' , will be further from the town centre than 'South Street' etc. High Street is obviously in the town centre, as will be Bank Street, Station Road/Hill will be by the station OR what WAS a station - a study of a map/Google maps will find you the approx location of the station. Abattoir Road invariably isn't too far from the station as the sheep/cattle etc often arrived by train. Market Place/Street/Square will also be town centre. Ditto Butcher's Row, and most other trades that are on Streets and Lanes. (Roads named after trades may be twee more modern locations) Castle will be at the top of a hill so Castle Hill/Road/Street usually leads from the town to it. Bars /Gates - are gaps in the city walls eg Above Bar in Southampton, obviously the city was a lot smaller in its day so edge of town centre there.
River Street - by the river. Likewise Moorings, Marina etc Bridge Street - look for the river or the railway. Friary/Church/Priory/Cathedral or School/College/University... - you know where to look!
Any road named 'Hill' will invariably be up or downhill. Valley Road - road along bottom of the slope.
From Victorian times especially 'Avenue' was popular, so outside of the immediate centre. Ditto Park anything - Victorians loved their parks - look for the green bits on the map and Park Road, Parkside etc should lead to it.
Crescents - Georgians onwards liked Crescents - look on the map for a curved bit of road, with bigger posher houses than the very centre of town.
Later still, so in the suburbs you have 'Estate' 'Gardens' 'Drive' 'Orchards' 'Parkway' 'Meadows' etc. so all on the outskirts. Boulevard is quite recent too, but can be an inner ringway sort of name where the original narrow road was demolished in the 1970s.. Most modern housing estates tend to have a theme eg trees, birds, poets , musicians etc, so find one and you'll find the others related.
Close - one or two can be very old, so town centre - or recent suburbia in my experience.
If stuck only then would I'd dive into a local shop and ask.
I do think that being able to read a map and find where to go is something inherited, my eldest is fabulous, started her with following the red road, 'when we go under that railway bridge there on the map, then we need to take the 4th road on the left' etc. When she started school despite being almost the youngest she was the only one reliably knew her left and right!
I absolutely LOVE maps and roads.
Recommended reading:
Mike Parker, Map Addict.
Tom Fort ,The A303: Highway to the Sun (Also view here )
*Edited to add I do have a Sat Nav but tend to argue with it too much.