Hi, Deborah,
Add me to the list of folks recommending an earlier start to your through hike. There are several companies which will transport your heavier luggage so that you can travel lighter with just a daypack. These carriers will take your luggage from Milngavie to Drymen on day one, and drop it off at your accomodation. They will continue to transport your luggage to each planned stop which you make along the Way. Although they don't provide accommodation, they provide a list of possible accommodation (B&B, hotel, hostel, campsite, etc.) along the Way, leaving the choice to you.
As far as sightseeing in Glasgow, there is so much to see and do there that you could spend a week there and not see it all. Personal favourites are the Cathedral, the Necropolis, Peoples Palace, Kelvingrove Art Gallery, Burrell Collection, Museum of Transport, Tenement House, the Hunterian and especially the Barras (weekends only).
My favourite restaurant in Glasgow is the University Cafe at the bottom of Byres Road. It has been in the same family for over 100 years, so they must be doing something right!
Best wishes for you travels. Be sure to bring waterproofs and stout boots!
Mike (Auchterless)