A walk through Old Stirling

We had afternoon tea in Darnley’s House, a quaint 16th century house in Old Stirling adjacent to the castle. 
( Rumour has it that we could soon we going into Level 4 – total lockdown- so we are making the most of our freedom).
 
It was said that Lord Darnley, husband of Mary Queen of Scot used to stay there when the Royal entourage was in Stirling.

 That’s the story but thanks to Google I have learnt this is a myth.
Over the years though the building has been used for everything from a dairy to a brothel to a tourist office and now a café serving home made food.
 
Just down the road is this impressive building, but I can’t find out anything about it. 
I wonder if anyone knows its history?