Should I log flights on separate lines if I park the plane between legs to different airports?
There are no hard and fast rules in the US about how and when to break up a flight like this, so do what makes the most sense to you.
In the military I would generally log individual sorties on different lines because there were varied mission codes, and sometimes we switched crews.  However, on a multi leg cross country I would log it all on a single line.  (As long as the multiple legs occurred on the same day.)