Here are some ideas for easy baby- and toddler-friendly day trips (max. car journey of 1 hr from the centre of Glasgow). We'll keep adding to this as time goes on, but please do send us your ideas.

Inchmahome Island
Tiny island in the lake of Menteith. There's a tiny ferry which runs regularly from April and September from the Port of Menteith. Just show up, and a ferryman will take you over. You can then agree what time you'd like to be picked up. It's the perfect child-friendly trip - lots of variety in short bursts. The ferry takes about five minutes, and you then have a 15-minute walk to the other side of the island. There's the thirteenth-centry Inchmahome Priory to explore, and picnic tables (and loos) at the beach on the other side of the island. The route to the beach is not buggyable, however, so you'll need a sling/backpack.
Historic Scotland Inchmahome Priory

Rozelle House, Ayr
After a walk at the beaches along the Ayrshire coastline, head to Rozelle for a bite to eat. If the fresh air has put you in the mood for a bit of culture, there are a number of art  exhibitions and local crafts for sale. The Rozelle Tea Room - walk round the back for ground-level buggy access - serves teas, coffees, soup, pannini, incl. child portions, and they have a number of high chairs. The staff kept my little one supplied with a steady stream of toys, and were even fine with him walking around opening all the cupboards....
http://www.south-ayrshire.gov.uk/galleries/rozellehouse.htm