Should Is bank of america a good bank, our should I go to a credit unit. I want a savings and checking account?

Bank of America is a good bank if you are an experienced user and can follow their rules
IF you keep low balances or tend to overdraft at least once a year - do NOT deal with them
They have free checking with either a $1,500 min balance or a monthly direct deposit
They have ATMs all over the US and their website has all the "bells and whistles" you could ever desire.

If you are new to banking. I strongly suggest a credit union.
Their fees (if you mis step) are much lower
Also credit union savings accounts tend to pay higher interest rates

There is no good bank, good credit union, or good bank account. You need to look at the totality of the bank’s services, accounts, and fees. Every bank and credit union offers several accounts with different features and different fees. Some banks or credit unions may have low overdraft fees, but high fees in other areas. Some accounts waive all fees if you maintain a minimum balance. The minimum balance varies from institution to institution. Other accounts have a monthly fee, but no fee on each transaction. Other accounts have no monthly fee, but a fee for each transaction.

Some banks have a large number of ATMs which you can use without a charge. Other banks have a charge for ATMs.

I suggest that you visit several banks and credit unions and speak to the customer service personnel. Bring a written list of questions which are important to YOU. Find out the features and charges of each of their accounts. Find out how many ATMs are available, and whether there is a service charge for using the ATM.

Make sure you get everything in writing. Do not accept anything the customer service person tells you verbally.