Am I okay to claim the American Opportunity Credit and Education nonrefundable credit while doing standard deduction? My wife just graduated and has not claimed this yet

Yes, you can get the nonrefundable portion of the American Opportunity Credit and take the standard deduction.  The American opportunity tax credit (AOTC) is a credit for qualified education expenses paid for an eligible student for the first four years of higher education.  A student (or parent) can get a maximum annual credit of $2,500 per eligible student (max 4 times or tax years).  If the credit brings the amount of tax you owe to zero, you can have 40 percent of any remaining amount of the credit (up to $1,000) refunded to you.  

The rule is that the American Opportunity Credit can only be claimed 4 times for a particular student. If your wife was a dependent of her parents, her parents might have claimed the credit for her tuition. So it might have already been claimed 4 times for her, by her parents, even though she did not claim it herself. If her parents claimed it 4 times for her tuition, she cannot claim it now, even though she never claimed it herself. You will have to ask her parents whether they claimed it.