Manchester is VERY well stocked for cafés, many of which are regularly full of trendy looking people with MacBooks as mentioned by various others.
One that hasn't been mentioned is ManCoco - a roastery with cafe under an archway near Deansgate Locks and Home (which is also a good hang-out).
If that's not your style there are plenty of non-hipster alternatives ranging from formica to fabulous. Richmond Tea Rooms in the gay village is a veritable trip through the looking glass.
Further afield, Chorlton has the Art of Tea and Barbecue (another roastery), Salford has Lupo, Gatley has Coffee Fix, and Ancoats has the Ancoats Coffee Co. All highly recommended.
Here's some (exactly the same as what we've all been mentioning) pointers from the local rag.