We stayed at Spier for 2 nights about 2 weeks ago. We enjoyed taking our 2.5yr old girl to the Stellenbosch market at Oude Libertas on the Sat moorning and had lunch there. Was lovely. Also had brunch at "8" restaurant on the Spier estate - has a lovely grassy area with a wooden jungle gym and swing (sort of). Took her to the Cheetah farm and also went strawberry picking at farm nearby.
You can give Vredenheim a try. I love going there - they have ducks and a small playing area for the kiddies as well. But the main attraction is the LARGE lawn area for kiddies to run/crawl/walk around on.