There is so much scenery near Stirling that you do not need to travel as far as you think - we are on the border of the Loch Lomond and Trossachs national park.
Scenery: head out to Loch Katrine via Callander and back via Aberfoyle.
Callander: go visit Bracklin Falls - basically a short mainly flat walk out of the carpark to the east of Callander. Marked on maps, easy to find. Callander itself will be half closed, but a lovely spot. Great cafe at Ben Ledi Coffee and superb bakery at Mhor.
You then head out via loch Venechar and the Great Trossachs Forest - lovely place, worth a stop at Brig O'Turk and walk up through the village towards the Glen Finglas Dam.
At Loch Katrine visitor centre / pier there is a short walk from the car park at the steamer up to a wonderful viewpoint, or just along the loch itself on the flat tarmac (private) road without traffic.
The way out will take you over the Trossachs road - take time to stop and look at the views, including the start of the (closed for the season) Forest Road. David Marshall lodge is great, decent cafe, lovely short walk to a cracking waterfall even in bad weather. With a load of kiddy play things on the way around.
Then onto Aberfoyle, but turn west towards Loch Ard. Ard feels like Canada....worth going along to the parking at the community hall at Kinlochard as the view is great. Aberfoyle has a few nice shops and worth a stop.
Then as you return back towards Stirling you will pass the only lake in Scotland - the Lake of Mentieth, and some lovely villages, finally the ace farm shop, cafe and kids play area at Blair Drummond Smiddy. You could also go via Doune again, where you can wander around the castle, famous for Outlander, Game of Thrones and Monty Python.
Second day I would also head north on a big loop - head to Killin (Falls of Dochart, lovely walks, properly HUUGE highland scenery) where you are most likely to see snow as Ben Lawers towers over the village and is 10th highest hill in Scotland and site of an old ski resort. Then along Loch Tay, if you have good weather and feel brave head over to Bridge of Balgie (ace shop and cafe) and travel down Glen Lyon which is the Longest, Loveliest and Lonliest glen in Scotland. From here you end up at Fortingall (one of the oldest trees on earth), and turn north again for the hop over to Loch Tummel. Take the north shore of Tummel to stop at Queens view, on to Pitclochry which is a modest sized spa town and will still be busy. As you head south you will stop at the Hermitage for a brilliant short walk in the trees (tallest in the UK) and sheltered from weather, finally popping into Dunkeld to explore the lovely bakery, cafe and riverside views...More driving than day 1.