There is a lot of sun and little shade so you need sun tan lotion. Baseball cap?
If you plan to stay late sometimes it gets cool so a sweat shirt might be nice. Jeans are an option for the sun during the day and possible cool temps at night.
I believe that bags up to some size are allowed but check on the USTA website. If you don't have anything to inspect there is an express line to enter.
This site also has draw sheets & the day's schedule to print and a map of the numbered courts. But the schedule may not be available until late tonight/or early tomorrow morning.
There are many things to see on Smartphones also, current match scores - maybe someone will suggest. LAST YEAR I SAW A WOMAN DROP & LOSE HER SMARTPHONE UNDER THE STANDS THROUGH THE SEAT OPENING.
Food - there are some turkey salads sold between the Grandstand and Armstrong that are very good (the same concession is also the first on the right after entering). Great ice cream cones are about $9........... Bottled water $2.50-3.00. They have a shortage of water fountains and there may be long lines for a few of them. Buy a bottle of water outside the gate for $1 and carry it in. Keep the bottle to refill. Don't wait in restroom lines, walk 2 minutes to find others.
I going also, have a great US Open!!