What is best location for an Airport Extreme?

If I moved the Airport Extreme to a more central location feeding it with coax from the router, would the reception downstairs be better?

Sure. Any WiFi signal loses strength and speed the further that it travels or encounters any kind of obstruction like a wall, heavy furniture, etc.

5 GHz signals are faster......but much weaker than 2.4 GHz signals......so 5 GHz will only work well when devices are in the same room or close proximity to the router.

The AirPort Extreme will need to connect back to the DSL router using a wired Ethernet cable connection. Ethernet can be run up to 300+ feet (100 meters) with virtually no signal loss.

Co-ax cable might work if you cannot run the Ethernet cable and have Ethernet to co-ax adapters, but results will vary. Consider using Ethernet over powerline adapters if you cannot run the Ethernet cable.

A simple thing to remember as far as WiFi is concerned is that the more that you have line-of-sight between a WiFi device and the router, the faster and more reliable the signal will be.

Personally, I have 3 AirPort Extreme routers spread out over about a 2500 sq ft home connected using Ethernet and the WiFi is strong and fast at just about any location in the home. The exceptions are bathrooms where the WiFi must travel through a tile wall or a mirror (which is basically sheet metal).