Is it a double trailer or single? How old are the kids- ie can they get out and walk if you need to take the trailer off and manhandle it through a narrow gap, or walk up a short steep slope? How long/short a ride do you want? Are you prepared to ride on the road at all?
Loads of trailerable stuff round Reigate/Headly Heath/Box Hill/Tadworth/Walton without being too strenuous, and there's a few places you can stop eg carpark at Headley Heath, across the road by the cricket pitch then follow the tracks up onto Colley Hill then to the Reigate carpark, then reverse the journey.
Kids also quite like the trip from Ditchling Beacon to Jack and Jill windmills on the South Downs and back- not too far for them, and a bit of a runaround at various points.