Haven't been to Balboa park in a few years - is the Arboretum open? It has remarkable plants, and is centrally located in the Park. If you like unusual plants, it's worth a visit. There are many museums to visit, if you have a special interest. Ask ahead of time which are open, or if there are any special exhibits happening. There is/was a cooking school at the Prado. We had a spectacular outdoor meal there, prepared by students who worked very hard. It was excellent.
The WM location is actually south of Balboa Park proper, and is about three blocks north of Broadway, the main street through Downtown San Diego. Park Blvd is at what would be 12th, as it crosses Broadway. The closest intersection to "downtown" SD is at 5th or 6th and Broadway. So it's not far, if you want to walk. Driving around downtown is a hassle, as is parking. Renting a car for a day, on a day you want to get out and see the outlying areas, makes the most sense. While you're hanging in town, or around Balboa Park, public transportation or Uber/Lyft makes the most sense. As others mentioned, there are street people hanging around in the Park, and car prowls are common. No need to park there unless you expect to need that car.