Well, first of all, it's Stirling, not Sterling. Common mistake. But you're right, it would be cheaper to stay there, generally speaking, than in Edinburgh. Stirling is a nice town, and you'd be in close proximity to the castle. Stirling is like Edinburgh in miniature. Falkirk is good as well. You'd be close to the Falkirk Wheel, which joins the Union Canal to the Forth and Clyde Canal. It's an impressive feat of modern engineering.
The Premier Inn in central Stirling is quite nice, and it's next to the train station. You didn't say when you're traveling, but if it's not in high season, their rates should be fairly competitive, especially if you book on line. With Premier Inns, you know that you're getting a comfy bed, a good shower, and a very clean room. The farther ahead you book, the better their prices will be. They don't include breakfast in their rates, but you can purchase breakfast there for an extra cost, or go to one of the excellent cafes nearby. Or if you really want to economize, the Scottish restaurant (McDonald's) is a five minute walk from the hotel.
Have a wonderful holiday!