Iron bridge is nice and has Blists Hill (Victorian town) nearby.
Telford has a park that’s been done up and is good (has a soaker area if you go when it’s hot take towels!) there’s a decent set of food places right next to it too.
There’s Telford wonderland which has all fairytale cottages and characters, a maze, a couple of small rides etc.
Hoo farm- lots of animals and sometimes has events on (near wellington)
RAF Cosford (the train station is a 2 minutes walk if you don’t want to drive)
Attingham Park - lots of lovely walks
Hawkstone Park - not good for pushchairs
Kids fest is on in Telford and Shrewsbury each year which is quite good.
Telford ice rink / bowling alley (rainy day ideas)
Much wenlock is pretty but there’s not much to do once you’ve walked up the one road and looked around the ruins.
Ludlow- there’s the castle, a few nice shops and the market. They have a festival each year too.
Long mynd and carding mill valley are nice for walks.
Kinver Edge is nice for walking too but just out of Shropshire.
There’s a giant inflatable place open over the six weeks in Four Ashes ( near junction 2 of M54)
Weston Park has lovely grounds and a decent kids play area and a steam train ride.
Cannock Chase is a bit further but also has nice walks, a Gruffalo trail and go ape.