i dont think it should be on new texas. a tattoo shop seems more like it belongs on tavros or tarkus, maybe more than one planet.
perhaps have special tattoos for treated people?
What makes you say that? New Texas makes the most sense to me, followed by Tavros and Zheng Shi.
Tavros only gets a nod because it's a big affluent civilized area where it makes sense that there'd be a tattoo parlour. You could slap a tattoo function into the hairdressers without much fuss. Zheng Shi makes sense because it's a hive of gangs and pirates; it could have a rodenian tattoo artist who does cheap or exotic tattoos but gives you a random infection each time because of her shitty parlour (or, for custom text tattoos, a chance for a typo).
New Texas makes the most sense to me because it combines the early-game accessibility and metropolitan amenities of Tavros with the theming links of Zheng Shi; cattle are tattooed and branded, and New Texas is built on body mods and packed with exhibitionist stuff like the stocks and cum pumps. If piercings don't show up (more) on New Texas in the future, I'll be surprised. Hell, Gianna could move to a different space to offer tattoos in the evening, frustrated that her artistic talents are wasted on a planet where the only ink anyone wants is CUM DUMP or BULL ON TAP or some variation of a crude cartoon heart with a name on it. Or repurpose one of the cumpump sisters - they run a "branding" parlour on their day off. Or use one of the duo you meet with them in the shower.