that's a lot of questions! haha. get a hotel on new year's day? there will be fireworks and it should be really awesome for a proposal. gather some friends too, yours and hers.
Hmmm. For me a good proposal would be something intimate and very personal to both of you. My hubbie took me picnic-ing under the stars because that was one of our favorite past times. And when we were stargazing he suddenly proposed.
for the proposal. i guess it would be much better if you do it on private and just between the two of you. that way, it'll become more intimate and sincere and will probably become really memorable for both of you.