What areas would you expect to be at their best on Oct 15 -20?
Well, there is plenty to see in fall, including autumn colors, if the weather cools, which is always the case to predict exactly the dates for autumn color, but late Oct may be good. The perennial garden and the demonstration garden are usually full of flowery displays, and both are in front (either side of the great lawn) of the conservatory glasshouse. Chihully glass exhibit will still be in full force within the Conservatory Glasshouse as well as some glass sculptures in the library bldg. 6th floor exhibit hall (4th floor also). A couple of sculptures near the main entrance, one in the fountain (tram is there too) to gaze at. The tram ride gives an overview of the garden, and i believe will go through the forest of conifers and hopefully colorful deciduous trees. A peaceful walk in the forest may have some color, but still depends on the weather temperatures.
Hope this is helpful.