Hi woody.
Swanage is not too far from Southampton & the Swanage railway is well worth a visit. In the opposite direction is the Bluebell railway & that is a great place to visit for all things steam. Something slightly different is the Hollycombe Steam Collection at Liphook in Hampshire, which has narrow gauge railways as well as traction engines & steam-powered fairground rides etc.
Also worth looking at the following websites:
www.uksteam.info gives details of steam-hauled trains on the main line, some of which will be passing through the Southampton area.
Also search for UK & Ireland heritage railways - this is a website that lists & links to all heritage railways in the UK & Ireland - very useful for what's local to you plus others if you're ever elsewhere around the country.
Hope this helps.
Regards,
Tony