It depends on what you are planning to do with this savings account. If you and the child want access to it anytime, then open it at the bank.. . The following options should not be opened at the bank (because their rate of return is horrible and they don't offer that many investment choices to choose from).. If you plan to have the child use it for college only, then go to a financial company or directly to a mutual fund company and ask for a 529 plan (there's another one, but I forgot whats it called).. If you just want to send money to the child as "gifts", open a UGMA account at the financial company or mutual fund company. Remember, with UGMA account, money you give to the child's account are irrevocable. That means you have no access to the money, only the child does when he reaches the age of the majority (which is 18-21).