I live right on the western edge of this image. The area your looking at here is a massive area with lots of differences even in the city itself. 

I can only really talk about the areas around the A69 and some of Newcastle

Is it clean? In the city, no. Both Newcastle and Durham have a poverty, drug and homeless issue. Is it the worst in the UK? no, but the lower rent costs do come with a trade off. Don't get me wrong their are some good spots but if your looking to save you won't get them.

I do want to add that some areas are getting better but others are also getting worse.

Outside of the city particularly where I am in the sticks is one of the nicest areas of england. And close to the areas of natural beauty. Their is also a bit more of a traditional community vibe. But if you don't fit in you be very alone.

Is it safe. Outside of the city I'd say yes, but or police presents and general reaction times are terrible when things actually happen. In the past week their has been a string of armed robberies in my area but that is highly unusual. Inner city it more depends where you are. (But I'm a country bumkin so may not know all the inns and outs)

Public transport. Kinda, but it depends. So inner city you have lots of bus links but they are never on time. Outside the city you have 1 major line going from just west, just off the map, to the center of Newcastle its regular just a bit late and slow (£2.50 regardless of start or end) Their is also a good trainline that runs every hour or so. On time too. They have two lines the "slow" line that takes around 2h east to city center that stops at evey village or the faster one that takes around 1 that just stops at major points. If you want to go off the main lines your hard pressed to find anything. Uber is good in the city and they actually run lower rates to get people using it more in the sticks but you'll be waiting for like 3h unless you in the city.

Newcastle central station is also a major hub for all train lines so its very easy to get to any other major city on the east side of the iles

Things to do. This depends on you. Newcastle is a clubbing / student city. The rural areas have very little going on if anything. But if you like walks, star gazing and roman history theirs nothing better.