Congrats on your promotion!
I couldn't find a Knights Inn near the Dome, the closest one I could find is Ferguson and you don't want to stay there.
America's Best Value Inn is pretty much across the street from the Dome, but IMO, I wouldn't stay there. I'm super picky when it comes to hotels though. Is your company going to comp you for your trip? Do you have an allotted amount for a hotel? There are lots of nice hotels in the area, but they are definitely going to be more pricey.
Attractions...the Arch as you said, I think you may have been referring to the Botanical Garden.
Here is a link that should help.
I would plan on freezing temps.

It's hard to say what it will be like at the end of October, sometimes it's really warm, sometimes it's not. More than likely you will need some long sleeve clothing, jacket, etc.