SOU is not that good for photographers – there is an observation gallery inside the terminal (turn left and up the stairs) but shooting through glass is not always the best option.

There is multi story car park but staying there for more than a few minutes will attract the security who will move you on. you could stay in car but you might need a 2nd morgage to get out.
First 10 mins however are free – just enough time to get to top level, get a pic and get out. (assuming there is anything worth taking a pic of)

At the northern end, towards Eastleigh (runway is 02/20) the Campbell Road bridge can offer some interesting shots although you will need to be careful where you park as the bridge is narrow and quite busy.

as the southern end there is the White Swan pub which can be reached by driving pass the airport keeing the Ford factory on your left, mini roundabout turn left and follow that road, the pub is on the left.

There are a couple of aviation enthusiast groups based locally (Eastleigh, Bishops Waltham, Gosport are 3 I visit) with regular meetings, talks, slide shows etc – if you want any more info then let me know.