Hadrians Wall - park at Steel Rigg car park and walk to Sycamore Gap or for a longer walk continue to Housesteds Roman Fort. Alternatively, drive to Housesteads or Chesters Roman Fort (both English Heritage). It’s also not too far to Wheelbirks that do great ice cream.
National Trust - gibside, wallington (can hire bikes), Seaton Deleval, cragside are all great for days out.
Alnwick is less than an hour from Newcastle and there’s the castle, gardens (they are doing a wizard of oz themed trail this summer), Barter Books and the beach at Alnmouth is lovely.
Spend a day on the quayside - Newcastle Castle/keep, Baltic, Sage, Millennium Bridege.
Riverside park at Chester-le-street is on the way to Beamish and has a splash park (think you have to book slots this year).
St Mary’s lighthouse in Whitley Bay or Souter Lighthouse north of Sunderland are both great.
National Glass Centre in Sunderland have some great summer activities planned. You could combine that with Souter Lighthouse and a walk up Penshaw Monument.
South Shield - funfair, Marine Park with boating lake, play parks & mini railway, great fish n chips at Coleman’s and ice cream at Minchellas plus good swimming pool, bowling alley, soft play, mini golf.
Water sports such as kayaking snd SUP at Tynemouth, Roker (sunderland) or Seaham.