If there are spaces available, you can park via ParkMobile on Walnut between the bridge and 33rd street, at roughly $10 for 8 hours.
The closest visitor lot is at 34th and Chestnut.
As there might be a lot of people on campus over the weekend, you may want
to reserve Parking via ParkMobile:
https://app.parkmobile.io/reservation/40114822
Rates are:
Monday-Friday: $23
Evening & Weekend rate: $19
There are various other visitor lots that can be reserved ahead of time:
https://transportation.upenn.edu/visitor-parking
https://maphub.net/PennTrans/upenn-transit-parking-2