Someone told me you shouldn't visit a cemetery on Friday. Is this correct?
More generally, are there any other days (holidays, events, etc) that you shouldn't go to a cemetery?
In Shulchan Aruch there is no mention of days that one cannot visit a cemetery.
There are Halachot that apply when visiting a cemetery on various days.
One then continues with Tziduk Hadin - which is not said on days when Tachanun is not said - including Erev Shabbat and Erev Yom Tov. (Kitzur Shulchan Aruch 188:14)
This may be the source of the rumour that you heard.
Since one must be happy on Yom Tov and may not be sad on Shabbat, one probably should not be visiting cemeteries on those days.
That said, (as mentioned in the comments) the Rambam, Vilna Gaon and other frown upon visiting a cemetery, if not for burials.