In real life, I don't particularly like tattoos in general, although I respect them for the art that they are. In terms of a game, however, if a character is one that would likely have tattoos then give them tattoos. Personally, I always wanted a partner with a copy of "War and Peace" tattooed on their back. That way I would have some incentive to read old boring classic literature.
Tattoos are hot as fuck! Tattoos and piercings, hell yes. Though I guess it does matter the level of tattoos. Like if it's full face covering, probably not. Though I've also seen some that look really good.
Covered by them does NOT look good and neither do tramp stamps. Not having any looks best. Same with non ear piercings. That's how women in the 70s and 80s looked better than after. On the other hand, not shaving pubes...
I really don't look much at that. There are a lot more thing I will consider first than a tattoo. Still it would depend on the amount of tattoos and the type. If she is all covered in tattoos; then, no thanks. Same with really offensive or crazy tattoos.