My best tip for Newcastle is on the Metro. No doubt you already know this anyway, but the Metro cars are similar to the DLR with views out the front available. My recommendation heading to South Hylton would be to try and get those seats at the back of the train on the outward run, ready to enjoy the forward direction back to Newcastle.
Another tip is that the platform change at Hebburn is via a footbridge, but with the long ramps it takes a fair bit of time to do. So I'd not plan for too tight a connection there.
Tynemouth and Whitley Bay are nice stations, worth a visit if only to see how vastly different it is now compared to how it would have been in BR operation.
Somewhere around the Longbenton area, the Blyth and Tyne freight line runs alongside the Metro. Same story around Jarrow.
Heworth needs a mention. I don't know know if they're still as bad, but the public lavatories outside the station certainly used to be notorious for the strong stench. Only ever recommended to use them in a desperate situation, and that was just for fluids release. Anything else you'd need to be beyond desperate...

Of course, this was a handful of years ago, so it could all be better by now, however I am doubtful.
Heaton depot can be at least partially viewed from Chillingham Road on the Metro. I do believe there is a better vantage point very close to the same station, although I confess it's been too many years since I went there to remember this for sure.
I'm of course assuming it's still there, but going back to Hebburn briefly, there is also a small Asda a few-ish minutes walk away. Could be ideal for some short-notice snacks/fluids purchasing, that kind of thing. Mind you if it's open currently, there is a small Sainsburys on Newcastle Central too.
Overall, I liked the Metro on my visits and I will have to make a trip to sample it again before the new trains arrive. I seem to remember I have a few years to go yet for that. It's a good value network, and I suspect you'll enjoy it.
In terms of tips for Newcastle itself, I've got to be honest I've hardly spent time in the city, so I can't really help you there. The few times I have been there, that weren't rail-based days, featured pubs and beers. So I don't recall too much of that

Other times involved stepping off the overnight Megabus and straight to the Metro to race over to Sunderland in time for the Grand Central HST back to London. Ahh the days when I could afford to turn up on a last minute trip to London, get a short notice Megabus fare to cover me for hundreds of miles and then still afford an on the day GC Only fare all the way from Sunderland to London. One feels a fair bit of nostalgia coming on this evening...
I will say this much though, have an amazing time!