Robert, the two attractions you mention are both in Beijing, both are worth a day to experience them and savour them. Read up a little before you go and attempt to understand why these places were built and why so much swealth was invested in them.
I also suggest seeing the Temple of Heaven. If you stayed in an area like Chongwenmen (there's a good Novotel Hotel there, rooms likely start around A$100-150/night) you can walk to both the Palace (Forbidden City) and to the Temple of Heaven, and there is a subway station adjacent.
Wide angle view of the Temple of Heaven
Behind the Palace there is Beihai park, also worth nearly a day to see all the pavilions which formed part of the Imperial pleasure grounds, such as this small pavilion.
This park was started about 1000 years ago and has been added to ever since.
and around the Palace is the Hutong area, changing rapidly, but worth seeing.
And, not far away (again you can walk) is Qianmen - (men means gate).
There is a restored Gate part of the old wall (now mostly demolished)
and a restored old shopping street
and, not far from that mentioned hotel is a section of the old wall that was not demolished.
And, still within walking distance is the Pearl Market (near the Temple of Heaven) - with all kinds of stuff for sale. For me the levels with Chinese art and handicrafts were the best
I think you'd find the Summer Palace worth visiting (another day).
Longevity Hill, Summer Palace
The long Corridor
At this palace, you can find a pavilion where Guangxu, the second last Emperor was imprisoned by the Dowager Empress Cixi and likely slowly poisoned to death with Arsenic.