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Road directions
It is situated just off the A6 (left if travelling towards Manchester, right if travelling south) a few miles south of Manchester.
Parking
This being a commuter station perched on top of an embankment parking is very difficult and the best bet is to probably park in nearby Stockport (again off the A6) and get a local Manchester bound service to the station.
Public transport
Levenshulme is served by a frequent Northern local service from Manchester Piccadilly (many connections here) which has a roughly 20 minute frequency Mon-Sat and no less than hourly on Sundays. You can also get through from the south from Stockport
Amenities
Due to the nature of the surrounding area I would say it would be very likely to have a newsagents nearby for snacks/drinks etc. But this is unconfirmed.
Accommodation
It would be advisable to stay again in nearby Stockport or Manchester.
Like all north/south lines the opportunities lie in trains travelling south, away from Manchester. The light is best in the afternoon or evening, although evening shots will be limited a certain times of the year as the line is flanked with trees. Catenery is not a problem as being on the platform you are already within the spans. By standing on the north (Manchester) end of platform 2 you can get trains travelling on the slow and fast lines going south and also get the back of units going north on the fast line, but trains on the northbound slow line are a little close to get a decent shot. This place is favoured as you can take the picture off the end of the platform and show no evidence that you are even at a station. You can of course go to the other end of the platform where there is a curve in the line and get trains going north, but the sun will be against you unless it is a cloudy day. There may be a little traffic noise and general city sounds in the background.