It is actually difficult to predict if any Covid related travel restrictions are still in effect in April and May next year, but assuming they are not:
Provided that you are a US citizen (if that is what you mean with 'American woman'), you will need an e-Visa which can be applied for online. You will get a multiple entry visa, with which you can enter Turkey on both days. During the last years, Turkey has several times suspended visa issuance to US citizens reciprocally to Donald's random discrimination of Turkish citizens. Depending on who is in charge in your home country and how your administration behaves, you would have to check the situation shortly before you travel.
Subway and rail connections are currently being built to Istanbul Airport, but you should be aware, that as of now, the only options for travelling between the airport and the city centre is by bus or taxi. You should count at least an hour by taxi to get to the city centre and during rush hour, the trip can easily take an hour and a half or more. The buses are even slower. If you add that up with the expected waiting times for immigration and security checks, I am not sure if you will manage to do much in the city on your first stay of just 8 hours.