Newcastle is not the most obvious tourist destination, people seem to be put off by the language barrier; but ah divvint knaa wot there on aboot man. It's a good thing the road signs aren't in Geordie as well though. Newcastle is certainly worthy of a weekend visit, especially if you like things big; by English standards there are big bridges, big buildings, and big portions of food. I recommend stotties in particular--a sort of big bread roll.
The big attractions for tourists are the Life museum, which offers interactive rides and displays; an outdoor ice rink (in the winter); and the quayside, with the world famous Millennium Eye Bridge and the new Baltic arts center--entrance is free, but you need to book in advance for the top floor restaurant. These two features are key to Newcastle/Gateshead's bid for City of Culture 2008, quite ironic really as your average Geordie wouldn't know culture if it bit him on the ass. The most popular Geordie activities are drinking, smoking, and raving about the football team.
If you're visiting in warmer months, hop on the metro and head out to Tynemouth, which has the best sandy beaches in the area, and if it starts raining--which it probably will, the sheltered sea-life center is also nearby. A metro stop away from Tynemouth is North Shields, the best place in Tyneside to experience fresh fish and chips, you can virtually see your cod caught and cooked in front of you.
Newcastle has a reputation for being a party town--the two main club and bar areas are the Quayside and the Bigg market. Most clubs are pretty similar however--dance music, ugly people, and sticky floors--so be careful where you go.
A final word of warning--don't be tempted to try Newcastle Brown Ale, many people believe it is just water dredged from the river Tyne. If you are in any doubt, just try speaking to a Geordie who's had a couple of bottles--howay man, it's yor torn to get the booze in.