Hi - sure others will have suggestions...
Loch Leven has new route - other forumers have written about.... could do day trip. Bus trip and can do in a day.
Waterfront at Dundee is good to cycle and had a pub with play area if weather changes. Plus other things to see. Don't know about bike hire but there must be...
(Glasgow waterfront? Bike hire?)
Aviemore has bike (+ski) hire and some new paths around Rothiemurcus Estate (I've heard). Train is under three hours from Edinburgh - expensive though. Try to get a through train otherwise you will have to trudge through Perth Station. That would mean overnight stay but good for children. SYHA has family rooms and other hostels there and hotel offers.
When your toddler is older then a cycle from Aviemore to Carrbridge can let them clamber at the landmark centre... My daughter loved that.
Loch Katrine has traffic free road and bike hire. No public transport though.