from the shortest way to longest:
sono (alto/a) uno e 60
sono (alto/a) un metro e 60
sono (alto/a) uno e 60 centimetri
sono (alto/a) un metro e 60 centimetri
if you add "centimetri" it sounds like you want to be very precise.
the first and the second are the most common.
sono alto/a 160 centimetri
it sounds a little odd, but it's ok.
Maybe it could be used if you went to a tailor or for a medical examination, but you can still use the previous ones.
if you are talking about a child you should say:
mio figlio è alto 50 centimentri