What a lovely idea.
You don't say where you are from as that could give us some clues to help the surprise.
But I should advise you that many places will close early on NYE (and the last flight on the eye is in the early afternoon before it closes in preparation for the evening fireworks and before they clear the ticket only zone to watch them) and that lots of attractions such as the British Museum and National Gallery will be closed on New Years Day and that as it is a Sunday then Sunday trading laws mean that many of the large shops are only open for 6 hours (if they choose to open that is)
I'm not trying to put a downer on your trip but you may just need to plan a little more in advance than visiting on any other weekend (apart from Christmas weekend) of the year.