In Lima you find banks nearly at every corner. But finding a reliable bank is as difficult as in any other city around the world. Being here only on holidays, you might not need a bank at all. For changing money you should better use exchange offices anyway and for drawing cash use ATM's that are placed all over the city. If you are a customer of an international bank that is present in Peru you should preferably use their ATM's. That way you can most probably save the sometimes quite high fees for international withdrawals. Check with your bank at home what charges you have to expect before you leave!
Opening an account is easy when you are a Peruvian resident. As far as we could find out, most banks have tightened their policies in the last years and don't allow tourists to open an account anymore. But as usual here the exception proves the rule. If you can open an account, be aware that banks in Peru charge literally for everything and sometimes their service leaves a lot to be desired. So check with the different banks on what they offer, so you can determine which one meets your needs the best. Bank debit cards and online banking are standard. Compare rates and take care of hidden charges!
Listed below are only a few of the bigger national and international banks with some of their agencies. For more info please check their websites, but unfortunately most of them are only available in Spanish.