Strong 2nd for a good tattoo shop.
Their piercers are trained and certified and spend YEARS doing this. Yes. It's more expensive (Around $30), but they're also not being done by the minimum wage girl who had an hour's worth of training. It's REALLY important to line up the holes so that as your baby grows they don't become all lopsided. A good tattoo shop is also INFINITELY cleaner than any option outside of a doctor's office (aka they practice the same sterile best practice that medical professionals do).
Remember; ideally, you want to get piercings done at or BEFORE 6mo old (so they can't reach them with their hands, and so that by the time they become more self aware the holes are both completely healed AND it's no biggie/ completely normal).