If your children are smaller (under 10) then I'd highly recommend a drive up to Bewilderwood, if you can read one of the stories then even better, it's a fantastic day out.
Park at Walberswick, you can get crabbing bits from the hut in the car park, nice clean public toilets in town too, once you finish crabbing you can go on the rowing ferry to Southwold, make sure you go up the (Grandpa in my pocket) lighthouse. RSPB Minsmere is also near Walberswick.
DD wasn't a fan of Southwold maize Maze but I thought it was a nice day out with play equipment for children and then we watched a show at thorrington outdoor theatre.
You can get the train from Beccles to Oulton Broad / Lowestoft or Norwich and its a lovely journey and you often see deer and birds of prey. The drive to those destinations is easy too.
As others have said Beccles lido is great but I believe they are shutting the heated pool soon for maintenance before opening for cold swimming.
If you have any horse lovers then Pakefield stables is always a hit with holiday makers to take a hack across the beach.