I believe I have the answer!
A part of me was a mode of transportation in the past.
In the past an OX would have been a common way to transport your goods.
A part of me is the mode of transport in the present.
A FORD is a modern-day motorcar.
A part of me is an important place in two fictional novels.
The SHIRE is the homeland of the Hobbits in The Hobbit and The Lord of the Rings by JRR Tolkien.
A part of me has acted in the movie made on one of the novels (described above).
Elijah WOOD played Frodo in the LotR movie series.
A part of me is active only in weekdays.
The STOCK Exchange is typically only open on weekdays and closed on weekends and federal holidays.
Put it all together and you have the place:
The town of WOODSTOCK in OXFORDSHIRE, UK.
As for the palace? It's not that big a place, so there's only one there! And it's:
Blenheim Palace, birthplace of former British PM Sir Winston Churchill!