The station in Marburg is surprisingly seedy for a small tourist town. When I arrived, on a Sunday morning, the streets outside the station were full of drunks and deadbeats, and the pavement was strewn with beer bottles and broken glass. Once you escape the station, which didn't feel dangerous at all, it gets rapidly more pleasant.
I wasn't joking when I said that Marburg has more stairs than Venice has canals. If you have mobility issues, like having a pram, then it will be a bit of a problem. There are paths, but they are steep. There are buses, if you can find them. And there is an elevator (don't you just love Germans?) from the new town and the old town on the hill. But it's not easy to find.
You can take a bus from the old market place up to the palace, but they only run about once an hour. So either you stay up there for an hour, or you have to walk down. The path from the palace is definitely NOT suitable for anything on wheels, except perhaps a 4x4. The road is rougher than a mud trail full of rocks.
Marburg, locals say, has more stairs in the streets than in the houses - this is actually an observation made by Jacob Grimm when he started studying ant Marburg university in 1802. Many walkways up the steep hillside consist of stairs. Some streets are accessible by car but many are not. Cobblestones are frequent and other types of pavement can be uneven, too.
Wear comfortable shoes, and watch your steps. High heels are a no-no in Marburg.
Marburg is not a good destination for people with walking difficulties. Taking the lift from Pilgrimstein and then walking along the two shopping streets, Wettergasse and Barfüßerstraße via market square, can be done because these two streets stay more or less on the same level. Anything further up, however, will be hard for people who do not walk well.
All ways to the Schloss from Oberstadt are either long stairways or steep cobblestone ramps, or a mix of both. Take the bus 16 from Rudolphsplatz/Marktplatz/Barfüßerstraße if you are unable or unwilling to climb the hill.
Of course residents can park in the old town, but if you visit Marburg you should park outside. Many of the rare parking spots in the old town are marked “for residents only” (= Anwohnerparken in German) and it would be rather tricky anyhow to place a car for people who are not used to this switching back and forth. To find empty space on one of the rare public parking like at the castle (photo 4) is pure luck! Don’t waste time and energy and most probably hassle afterwards with tickets and use one of the public parking garages. There is a big one in Pilgrimstein (street), the one I mentioned with elevator to the old town. It has five floors and there is always some space. Because Pilgrimstein is a one-way street (north-south direction), drive to Elisabethkirche and then into Pilgrimstein.
There are other parking garages or bigger parking lots, but this is the best for a day visit. In case you have booked a hotel, ask the hotel staff where you can park the car when you make a reservation. In case the hotel has a website, they will mention parking possibilities.