Manchester centre is not really the place, you need to head to Rusholme's (in)famous "curry mile".
Fortunately, this is a doddle to get to from the city centre (Simply head south along Oxford Road). Not more than 5-10 mins really.
Once there, the choice is quite something.
Overall the standard is quite good but personally I always found Sanam and Al Bilal the best places to eat in. The former does not serve alcohol (or allow it on the premesis) however.
Other places worth a look are Tabak (which does Nepalese food) and Hanaan which is a bit 'posher' looking but the food is no better than the others.