It seems that "make a visit" is not a common phrase, and I am not sure what is the difference between "make a visit to a friend" and "visit a friend". The following sentence is copied from The Guardian:
A huge 17.5m leisure trips are expected to take place on the roads between Christmas Day and New Year’s Day, as drivers make visits to friends and family, although the absence of commuter and commercial traffic during this period means the roads will be relatively quiet.
Also Ngram suggests that the phrase "make a visit to" is used.