Of course, the most notable site in Stirling is the castle. Stirling Castle is one of the most amazing structures I have ever laid eyes on. Workers are now repairing the buildings so we can see how they looked hundreds of years ago when they were first built. Truly magnificent.
From the hilltop on which the castle is situated, you can see the other most prominent building, William Wallace Monument. A towering piece built in the 1800s to honor the one and only Braveheart. Stirling is the city that saw some of his most famous feats, and so it is fitting to have this tower here. You can also see, but not visit, Stirling Bridge, where Wallace's army defeated the English in 1297.
A surprising, yet thoroughly enjoyable, place is the Old Town Jail. Here you will learn the history of the jail in Stirling, complete with tales of outrageous prisoners and punishments. The man leading you through the tour is a riot, changing costumes and accents in the blink of an eye.
Simply walking through the streets, looking at all the shops, is worth a trip to Stirling. You'll find just as high-quality stores and restaurants here as you will in Edinburgh.
Quick Tips:
There is a bus tour of Stirling provided by City Sightseeing that will help you get acquainted with the city. It is the hop-on, hop-off kind, and the ticket is valid for 24 hours. There is a discount for students and children 5-15 years old, but it only runs April through October. I took that one, but I'm not sure if there are any other tours like that. There may be, but I didn't see them advertised.
Best Way To Get Around:
The best way to move around Stirling? Your own two feet! Stirling is a nice, compact city. The only time you would need transportation would be to access Wallace Monument, since it is placed in a less-populated area.
A rather nice bus system is available with reasonable prices. There are also taxis, but they are more expensive and never seem to be around when you need one.
If you want to leave Stirling or are arriving in Stirling, there is a very nice train station. From here you can travel to a multitude of places in Scotland.