UKH

I may be going on an impromptu work trip/holiday to the Trossachs area in a couple of weeks. Could anyone recommend me:

1 - Single day circular hillwalks. Strenuous is good, getting to the top of something is good, reasonably un-busy is good, will have a dog so low concentrations of sheep are good. Would be aiming for 4-6 hours rather than 8-10.

2 - Beaches (loch or sea) which one could swim off*. Happy to walk a fair way to find something more secluded.

Are there any other things I simply must do in the area? I'll probably visit the Falkirk wheel as I am an incurable engineering nerd.

* I am optimistic that the weather will hold, though the dog will go swimming even if it's snowing.

Some walks: 

Stob a' Choin from Inverlochlairig

Stob Binnein, Meall na Dige, Meall Monachyle from Inverlochlairig

Meall an t-Seallaidh from Balquidder

Stuc a' Chroin and Beinn Each from Braeleny (possibly on the long side)

Ben Lomond from Loch Dhu via Comer (the summit will be busy, but the rest of the route will be deserted) 

Great suggestions. 

Meall an t-Seallaidh can be combined with Creag MacRanaich as a horseshoe around Glen Kendrum, starting from Lochearnhead. MacRanaich is a fine craggy hill, and you can add Meall Sgallachd on descent or ascent.

Also The Tarmachan Ridge starting from the North (The Glen Lyon side. Not the usual way, quiet approach and descent, and with a more remote feel to it).