I live in the Boston area so can't help with the questions about what to do, but the suggestions above look good to me.
At that time of the evening there are very few flights so Terminal E is very quiet. Security lines are non-existent. The BA lounge is still pretty busy and nothing to get excited about but most of the shops and food outlets close around 11-12 so there's nothing else to do either. I typically aim to arrive closer to 2h before departure than 3h.
The Plaza Premium lounge at HKG mentioned above does not need any membership, you can pay to enter. Something like US$20-30 if I recall correctly. Don't pay the extra for the breakfast as it's completely underwhelming. The showers are worth it though.