Parking depends largely on where you’re coming in from - I live east of Southampton, so I find that Priory Road is ideal. It’s not a long walk from there to the Rockstone and there’s a footpath between the Itchen and the railway to get you back from the ground. You miss the worst of the traffic both ways. If you’re west or north I don’t know, though from the north the same area is easily reached.
Can’t do post-match drinks unfortunately, but I’m sure the Goat will be available to lead you astray…