Literally NOTHING increases Fame except actor career!

I agree that it's definitely better to do things out and about. I thought my music producer sim wasn't getting much fame because he hadn't released that many songs, so I'd been having him spam a bunch out in the hopes he'd get more fame, but nope, didn't work. When Father Winter invited him out to a talent show and I played on of his songs on the radio, he got a way more fame in just that short amount of time.