Two nights only effectively gives a full day in a place. A lot depends on what your expectations are of Stirling and what you are wanting to do/see there.
Top of the list is always Stirling Castle and that can easily take up half a day. Just below and a few minutes walk , is the Church of the Holy Rood where Mary Queen of Scots worshipped Jand where he son was baptised. (He was teh one who became James Vi of Scotland and James I of England)
Almost next door to the church is the Old Town Jail which consistently gets good views.
Just to the south of Stirling is the site of Bannockburn where Robert the Bruce spectacularly defeated the army of Edward II (admittedly not one of the better English Kings and not a patch on his father!) There is a 20minute bus service from the bus station, taking about 15 minutes.
Alternatively catch a bus to the Wallace Monument for its views and the story of his defeat of the English at the Battle of Stirling bridge (remember Braveheart?) Go and find the Old Bridge too. (walk from Stirling)
There is also the ruined Cambuskenneth Abbey on the outskirts of Stirling and reached across a bridge over the river.
If you like exploring on foot, this website has details of Heritage trails and other places to walk around Stirling.
I would say that Stirling would repay spending two nights in... Longer if you want to pursue some of isn31c's ideas,,,