Bars depends on what floats your boat I guess, but some smart bars include Revolution (stunning interior), Tokyo just over the road is also a tidy place, but I've only really been when it's quite quiet - it doesn't seem the biggest of places, so when busy may be a bit of an ordeal. I would also suggest going to the Centurion bar at the train station (honestly, believe me on this one) - the decor inside is unbelievable, was also included in the Observer good bar guide in recent years. Good beers too! Hoko 10 on Dean Street is also good for some cocktails, great little booths to hide away in. The Trent pub, close to St James' Park (if you're at that end of town) is one of the best pubs in Newcastle as far as I'm concerned. Traditional boozer with great beers, free jukebox with so much good music on (think classic soul, groove, dance) - great laid-back atmosphere too. Oh, and for possibly the best views from a bar in the city, try the Pitcher & Piano. OK, it's a P & P, and they're everywhere (I think), but it's located at the Newcastle end of the Millennium bridge, right on the river with huge glass windows (well, being windows, they would be made of glass) and great for an early evening drink. The roof terrace may be off-limits in the current weather however. The Cluny in Ouseburn is prob my favourite bar in Newcastle - about a 15 minute walk along the Quayside and have a great choice of beers. The food's pretty good too.
I would avoid the Metro Centre unless you particularly enjoy shopping, plus it's not in Newcastle, it's in Gateshead, only about 15 minutes away. I live in Newcastle and I wear my Everton shirt about, so I wouldn't worry. Even the odd Sunderland shirt is seen here and there so I think you'll be fine with one of ours.