The Court of Chancery is where he was looking for his car—the garage attached to the courthouse. Perhaps he’d parked there previously.
But his car was towed away from closer to the train station—according to reports, it had been there since Dec. 13.
In any case, why would he leave his car in Wilmington and go home to New Castle without it (on Dec 13)? Perhaps he parked at the courthouse for court and moved it to the train station later in the day...but it still doesn’t explain him getting off the train in Wilmington and getting to New Castle without his car that was right there. Or why he would leave it there and get the ride with friends on Christmas Eve.
He may have left the car in the paid garage, because he didn't have protected parking at home. Didn't want to have to move the car every few hours to accommodate parking regulations. Friends in the city keep their car in a similar place, getting it out only for special occasions. Use public transportation or hitch rides everywhere else. Particularly if parking is difficult at their destination.