@fatfixie , a whole week in Hamilton? My condolences
Riverside museum in Glasgow is well worth a visit. It's the new home to the old Kelvingrove Transport museum and has a fantastic display of bikes hanging from the roof in a helix. Lots of cool cars and motorbikes as well and it's free. If you make it there, then Kelvingrove museum (also free) is not far and is also great, especially for the Spitfire hanging from the roof.
If you like old industrial stuff then Summerlee museum in Coatbridge is only 15 minutes from Hamilton and a good way to spend a couple of hours. My wee boy and his granny loved the old electric tram.
Nothing to speak of in way of cool bike shops that I'd go out of my way to visit.
You planning on riding? If you are in Edinburgh then Glentress would be an easy visit and has hire on site.
Enjoy the weather, it's not always like this. Probably why you left.