A great place to visit which is even free of charge is Chatelherault. It’s situated in Hamilton with easy rail access from Glasgow (there is a train station just outside the country park.
Chatelherault offers a perfect day out for a family (or anyone really) – with beautiful long woodland and river walks, an adventure playground, a garden centre with a rescued farm animals area (which carries an entry charge to maintain it) and the mansion itself which has a lovely cafe and an exhibition, as well as events for children of all ages.