The current schedule does not require any repositioning flights as there are adequate stations that can transfer 747s.
Historically the most common repositioning flight is
SFO-
ORD. This is because
SFO is the main hub of 747 flying and
ORD is where A checks are done.
HKG,
NRT and
FRA all can rotate 747s, so flying between the cities is not needed, but I wouldn't be surprised to see
SFO-
ORD pop up in the summer schedule again. It's used as a virtual spare route however so it can easily get downgauged to a 777 3-class + A319. The 747 is needed to cover Hawaii routes if a 777-200 2-class is down for maintenance as it is the only plane with enough capacity to cover the route. Also,
UA wants to have a spare 747 in
SFO in the morning and
ORD in the afternoon. The morning is used in case any of the international departures has a mechanical problem with an inbound airplane.
ORD is because the Asia departures are in the afternoon.
Other routes domestic routes can see 747s, but if you are searching for a 3 class plane, 767s and 777s appear on domestic routes more often (especially
ORD-
DEN).
If you have never designed an airplane part before, let the real designers do the work!