hbo go on apple tv

No, that is not a feature of the Apple TV. Nor will you be able to get it to work via airplay or airplay mirroring, HBO have blocked that feature for the time being.

As far as I know , there is no HBO on the ATV , however, you can watch HBO on your ATV if you have an iPad and a third party iOS app:

http://www.theverge.com/2012/3/27/2906004/comcast-hbo-apple-tv-xfinity-ios

Only for Comcast subscribers.

Have any idea why I can get the audio from HBO Go but not the video?

I believe my cable company, TimeWarner doesn't support AirPlay with HBO Go but find it odd I can stream the audio.

I'm experiencing the same problem trying to play HBO Go from my iPad to Apple TV, however, I have Verizon FIOS.

Audio is on by default. Video needs to be enabled by the developers. HBO have decided against implementing it, likely for licensing reasons.

Ironically, it does work with my MacBook Air.

Mac mirroring is fairly new so not sure on the criteria. I know for IOS mirroring the dev has to specifically block access.