They were advertising boat trips in Shrewsbury last time I was there a few weeks ago (my home town) and looked ok. there was a landing stage right by the Armory bar (lovely bar and lets small children in regardless of whether you are eating) near the Welsh Bridge. Avoid the Wetherspoons (Kings Head I think) if not eating as they won't let children in otherwise.
The Boathouse Pub is always popular by the riverside overlooking the Quarry (park) and the Quarry could be good for a picnic in nice weather, take some food for the ducks and grab an ice cream and there always used to be a small play area.
You could have a wander around the castle grounds too.
Alternatively, is Waterworld in Stoke too far?