The MetroCentre isn't strictly in Newcastle. It's about 3 miles away, in Gateshead. If you insist on getting a taxi, I'd guess at around �7 for the fare.
But it would be far simpler to hop on a train. The MetroCentre has its own rail station, which is just 7 minutes away from Newcastle. There are 4 or 5 trains every hour. The fare is �2 single or �2.30 return. If you're travelling by train to the area, you might find that there's hardly any additional fare (if any at all) if you book through travel to 'Metrocentre', rather than to Newcastle.
Chris