Sorry Dan to be slow in replying. I don't know whether this is too late for you, and it depends if you have a car or not. I would suggest you try to get to the Southside - up from what use to be the Valley Lodge hotel (sorry I'm probably showing my age).
Hope that helps.
Sorry Dan I'm afraid I'm rather out of touch with that side if the airport. Looking at Google maps if you head through the airport tunnels on the A538 you'll come to a roundabout just before the Airport Inn. First exit on left is Altrincham Rd and about 200yds up on the left there appears to be space for 2 or 3 cars (I think there's a gate to stop you going any further up the road.) Alternatively you may be able to park at the hotel itself.
Either way you'll need to walk up to the runway, but I seem to recall it's a well trotted path. Please ensure you take out anything that you take in - there a history of rubbish being left behind by people.
Try having a look at the "Announcements" page on Manchester Airport Spotters on Facebook Groups and you'll find a little more info. You could try phoning the hotel and see if they're able to offer free parking as I assume they are probably closed to guests.