Most banks have websites, and banks with branch locations usually list them on their websites. If you cannot find the information there, look for a bank phone number on the website and call the bank for the information.
If you can't find the bank's website, try the FDIC's BankFind https://banks.data.fdic.gov/bankfind-suite/bankfind page. It has office locations for all the FDIC-insured banks in the country. If you have the bank name, select the "bank name" search option, key the bank's name into the bank name field, scroll down just a bit and click search.
The basic information for the bank will appear as a search result. If there are similar bank names (there are a LOT of separate banks with similar names), you'll get a list. Identify the bank you are interested in on the list, then click the VIEW ALL OFFICES button to get a list of offices by state for the bank.
This tool only covers banks and savings associations insured by the FDIC. If you are looking for branch locations for a credit union, look for branch information on the credit union's website. Deposits at federal credit unions and many state-chartered credit unions are federally insured by the National Credit Union Administration. They have a search tool on their website (www.ncua.gov) that can be used to locate or research a credit union.