Should I exchange money at the Bali airport, or is it better to do it elsewhere? I heard that currency exchange rates are better at exchange shops in Seminyak downtown.

Your plan is on the right track. It's advantageous in terms of exchange rates to exchange only a small amount at the airport for tips and initial transportation costs, then exchange the rest at a money changer in Seminyak. According to reference materials, airport money changers have poor exchange rates, and money changers in city areas like Kuta or Ubud offer better rates. Since Seminyak is also in the city, you'll get better rates than at the airport. However, for safety, it's good to find a reliable official money changer in Seminyak like BMC. Avoid street money changers, and use official money changers inside shops or bank booths to reduce the risk of fraud. Another option is to withdraw cash directly from a BNI ATM at the airport. Since there are almost no fees and the exchange rate is reasonable, this method is also worth considering. If you have a credit card or travel card, this method would be convenient too.