Hi
@Little Rach. You can head to Newburn Bridge, then take an immediate right turn onto he Hadrian Cycle Route. It'll take you off road all the way into town, at which point you can head up St James's Boulevard. I think there's a cycle lane all the way up.
I can't see any other way, the path on the south side of the Tyne is not as well made and looks longer.
The Hadrian's path is direct, although it does take you across Scotswood Road a couple of times.
The path runs next to the Tyne, so you would need to veer north off it somewhere near the Arena - a bit of trial and error will be required to establish the best sequence of turns.
You could turn left a bit earlier opposite the Ford garage, and then right at the top of the bank towards St James's Boulevard.
But the left turn is a bit of a climb which you don't have to do if you stay on the path/Scotswood Road and turn nearer the Arena.