You could try the biscuit factory. Arts space with a cafe in the rooftop. Give them a call as they sometimes have events on.
The other places down in the Ouseburn area could be good: cluny, bike hub, ouseburn farm cafe. Possibly a bit far out for your needs.
What was The Sage (now The Glasshouse) has a couple of nice cafe/ workspace areas with power points & usb ports, good nibble food and coffee.
The Baltic has a cafe but it’s really noisy.
Phone signal inside the Hancock’s 4’ thick 1930s walls is a bit hit and miss. Cafe is not up to much imo. Same for discovery museum.
center for life is likely to be riddled with school parties.
Johan’s in fenwick’s is stuffed with blue rinse brigade borderline Nazis rabidly gossiping over the express and mail. Its other cafes are up themselves and won’t take kindly to having people loiter over a cooling cortado. Avoid. Likewise John Lewis.
Given your work location, Cafe 1901 in jesmond is nice. Noisy but full of vibrant trendy students pretending to busy on MacBook Airs. There’s a few others in jesmond. Jesmond dene cafe can be ok, but phone signal down there is patchy.
The airport itself is pretty nice. The main bar has good seats with power sockets overlooking the apron in a quiet corner behind Burger King. Metro bar is currently closed for refurbishment. Non-BA lounge is full of chavs binging on crap lager (unless you have sky team elite status in which case you get whisked to somewhere far more civilised.) BA lounge is BA lounge: full of empty bubbly, cucumber sandwiches and the unnerving sense you’re being done.