1) Go to the park and feed the ducks
This is a really nostalgic experience and always quite fun if you haven't did it in a while. It's really fun if you have kids with you too.
2) Picnic at the beach
This is great if it's good weather and there are so many beaches in South Shields you are bound to find something you like. The main beach is good for sunbathing and splashing about in the water, or go to the ones at Whitburn if you like to do things like rock climbing. You can always bring food or get some chips out which are really cheap.
3) Nature reserves
There are plenty of nature reserves about if you are quite outdoorsy and like walking. I go to the nature reserve or beach walking Molly most days out the week and find it so relaxing.
4) Go to the arcades
There's load of arcades along the seafront with loads of games. Penny machines if you like a challenge but are limited on what you can spend, proper arcades games if you're feeling flush.
The museum is a really good choice if you haven't been before. The one in Shields is all about the local history which is really interesting when you recognise the areas.
6) The ampitheatre
In summer there's always tons of bands and children's acts to see at the ampitheatre for free.
7) Bents park
Bents park tends to have better known acts on in the summer such as Sophie Ellis Bexter which you can see for free as well.
Hope these suggestions were helpful, let me know if you come up with any more!