I am (optimistically I know) looking for somewhere lovely with a babysitting service and/or near a nice restaurant that has space on New Years Eve within in easy-ish travelling distance from Buckinghamshire area.
hotels don't really offer in house babysitting if you are going off site to eat in my experience. you might find one that does good food and will find sitters for you if you eat in house but they are a bit like hens teeth to be honest. also you have left it very late - only 5 weeks away.
are you really going to find someone anywhere that will sit on NYE let alone at a hotel? good luck but not entirely sure you are going to find this. sorry.