Stirling is a small city that punches above its weight historically. It sits at the point where the Highlands and Lowlands meet, and for a long time controlling it meant controlling Scotland, which explains the castle and the battles and the general accumulation of history in a fairly small area.
Stirling Castle is worth the time. It's on a volcanic crag like Edinburgh Castle, the views are good, and the restoration of the royal apartments — including the carved oak medallions in the Great Hall — is genuinely impressive. The castle was a royal residence for much of the medieval period and there's plenty to look at. The National Wallace Monument on its hill above the Forth is visible from a long distance in any direction. It's a Victorian tower commemorating the Battle of Stirling Bridge and contains exhibits on Wallace and the independence period. The climb gives good views.
The Forth Valley has a couple of engineering attractions that are legitimately interesting regardless of your interest in engineering. The Falkirk Wheel is a rotating boatlift that connects two canals by turning boats through a full rotation — it's strange and elegant and worth seeing. The Kelpies nearby are large steel horse sculptures by Andy Scott, installed in 2013, representing the heavy horses of Scotland's industrial past. They're 30 metres tall and look better in person than in photographs. Both are accessible and well managed as visitor sites.
The Queensferry Crossing, where the Forth narrows between South and North Queensferry, is the newer of the three bridges there — opened in 2017, a cable-stayed design that sits alongside the Victorian rail bridge and the older road bridge. North Queensferry itself is a good spot to see all three at once.
For families, Blair Drummond Safari Park is a straightforward and well-run day out a few miles west of Stirling. Briarlands Farm nearby does pick-your-own and has good farm shop credentials. Dunblane is a quiet town with a medieval cathedral that's worth a look if you're passing through. The Forth and Clyde Canal towpath connects several of these places and makes for easy cycling.
Stirling is easily reached by rail from both Edinburgh and Glasgow, which makes it a practical day trip from either city.