The best nationwide bank, in terms of having a physical presence, has to be Chase.
Chase has over 5,000 branches and over 16,000 ATMs. In addition, many of Chase’s credit cards have some of the best sign-up bonuses and travel perks in the banking industry. Even their checking accounts regularly have nice sign-up bonuses.
The most significant thing Chase is lacking is checking/savings accounts with high-interest rates. If that is something you have to have, you may want to look elsewhere.