https://www.southampton.gov.uk/Images/Riverside Park map_tcm63-366731.pdf
https://www.southampton.gov.uk/people-places/parks-open-spaces/parks/riverside.aspx
Above is a link to Riverside park, and the map. It is free fishing throughout the park and above/ upstream of the A27 past the Swan pub and up to Gators mill, the Lower Itchen fishery.
The Woodmill center is roughly in the center of the park. Downstream of woodmill is tidal, the sea side, upstream is not. On high spring tides there is some tidal influence on the river but it's negligible.
Around Woodmill it's possible to catch Bass and Mullet one side of the road and coarse fish the other. Quite good Bass fishing on the sea side but not easy, waders and good local knowledge required. Don't forget there are four tides a day there. There are a few pier type structures.
The coarse fishing in the park and around the pub is excellent. LOTS of dog walkers, cyclists, joggers and others in the park. At the bottom end, by Woodmill there's a big car park and there's a lot of duck feeding goes on near there, needless to say bread is a brilliant bait in that area and the Roach seem to stay around for the daily feed, and the Pike.
There's mention in the park blurb about the Itchen walk or similar, this extends over 10 miles + of the river and is all free fishing as far as I know. Mostly it's on the navigation, I had a look at a stretch at Shawford recently, supposedly good for Grayling and if we get a bit of rain and some really cold weather soon I'll be giving it a go. Thigh waders at least needed, was there on a Saturday morning, no anglers! There's also a few free bits around Bishopstoke, Winchester and Twyford.
There's a good chance you might hook into a sea Trout or even a Salmon this time of year, so be prepared.
One of my favourite stretches of water, notwithstanding the crowds, some great viewing spots around the pub, you can see the massive Roach (I've seen 3lbers) feeding on the free offerings and avoiding the hookbait. The top swim, just below Gators mill is good but again, waders required, it's a lot deeper than it looks!!
Enjoy.