Yes, it's nice here! I'm a SE transplant too, and moved up because it was just, well, nice..! Cheaper housing, friendly people, the grotty parts are entirely avoidable unless you choose to move there), lovely beaches, nice countryside. Newcastle has everything you need without feeling overwhelmingly big/busy. It doesn't feel Big City to me, even though it has the facilities of one and a definite sense of a proper city centre. Nice architecture too, now it's all been tarted up a bit.
The rain feels comparable to the SE really. Most wet weather blows in from the Atlantic, meaning it's mostly rained itself out by the time it gets to this side of the hills. It's nothing like the NW.
It depends on your definition of hot. The average summer's day here tends to be about 5 degrees cooler than London. We do get some lovely days in the 20s (at which point all the locals start wilting), and it never feels sticky/muggy/oppressive here, but summers can be disappointing. Even if it's an overcast day across the country, grey and 17 degrees feels very different for a midsummer's day than grey and 22 down south. Budget for holidays. (Newcastle airport is at least pretty nice to fly from.)
Commuting into the city is fine (traffic at rush hour, otherwise it's unusual), and it's a nice city to be in. No rat race as you've said - those who want to race go south. Socialising here has been good, and people are easy to talk to, though I'm a slightly different demographic.
It's lovely living by the beach (for either bracing winter walks or lounging around in the summer pretending to be a tourist, then popping over the road home again), though I'd factor commuting time if that's important to you after a long shift. It's also very easy to live more centrally and just to jump on a metro (or quick drive) to the beaches if you know you're more likely to visit once a week than once a day.
The countryside is less "bucolic bliss" than the home counties, which I do sometimes miss, but the countryside still gets top marks. It's just more moor-like, with some pockets of woods and forest (including Kielder of course), but it's less leafy overall than the home counties, and slightly less of a sense of infinite footpaths to wander down. I'm not quite so blown away as most by the Northumberland coast - the beaches themselves are very nice, but the land around it is mostly flat agricultural land. Not very inspiring. Bear in mind that cars are essential for any kind of countryside outing, because the rail network is pretty sparse here and buses would take ages.
The "city" beaches themselves from Whitley Bay down to Roker are all absolutely lovely, and don't feel urban. There's a nice cliff walk from South Shields to Seaburn that feels surprisingly wild too. There's a lot of open space around.
I can't comment on nursing, but the RVI and Freeman are two of the top ranked hospitals in the country. Staff always seem cheerful when I go through the RVI, and it's a nice hospital to be in. South Tyneside rather less so.
Other than that, I'd say the cost of living difference is overegged. Housing is obviously massively different, but other than that there's not a huge difference. Groceries are the same, petrol is the same, energy bills are the same. Eating out costs the same as it did in London, but for lower quality food a lot of the time, though if we're comparing to a smaller town elsewhere in the SE maybe that difference won't be obvious.
The mix of people varies a lot by area. The more upmarket areas are spoken of a lot on here but it's places like Whitley Bay, Cullercoats, Tynemouth, Gosforth, Jesmond. Heaton is gentrifying now. High Heaton is quiet and suburban. Spitaltongues is bang in the city, without the noise. Same with Ouseburn. A lot of other areas still feel more "local" and I wouldn't be keen to live in them, even if the housing is much cheaper. That's most of west Newcastle, and a lot of east Newcastle. I'm not too sure about the northern suburbs - I think they're fine, if not des res?
No regrets moving here. The only thing I miss is a) a proper summer (anyone in England can complain about that but it feels more true here!) and b) the sense of career opportunity, and having a wider mix of people at work, although I shouldn't think that one would affect you!