Whether it's 3 or 4 nights, I think your idea of staying in Stirling is sound. You might want to spend some time in Glasgow before you go, though - there is a lot to see and do there, like the Kelvingrove museum, St. Giles cathedral and the Necropolis, among others. You could spend one night in Glasgow and see as much as possible, then take the train for Stirling, which is an easy 30+ minute ride from Glasgow Queen St. station.
Spend the day in Stirling, visiting the castle and the town, along with all the attractions there. The next day, head for Falkirk and the Kelpies and any other sights that take your fancy. If you have time, you could always take a day trip to Edinburgh and stroll around the old town (and the New Town, which is also lovely). I won't suggest visiting the castle, as you probably won't be able to get reservations this late, but there are a lot of other places to visit there. And it has a wonderful atmosphere that you can soak in just by walking around. Here is a link to my trip report, which talks about several of the above places, and also lists restaurants, etc. https://community.ricksteves.com/travel-forum/scotland/solo-in-scotland-trains-cars-and-ferries-and-a-wee-dram-or-two
ETA: All the places above are reachable by public transport. I do not think you would need a car to visit any of the above places (and you certainly would not want a car in Glasgow or Edinburgh.