There is a subtle difference:
1) Mi trovo in centro a Roma - it means in the politcal center, it's like saying "downtown" in the USA, it means maninly the most important area in the city, where there are all the government buildings.
2) mi trovo al centro di Roma - it means I am exactly in the center considering the size of the city, like saying "being in the center of a room", in the middle.
Of course, "Mi trovo in centro" is the one we hear more often, but even if some people would say "mi trovo al centro" it would actually mean the same thing, since nobody would say "centro" in the sense of being in the precise middle part of a town. So in Italy we just say:
Vado al centro
sto al cento
vado in centro
sto in centro
they mean the same thing and when we speak with someone who is in the same city like us, we never add the name of the city or town.