Hi Sanghamitra, You can cover Paris and Amsterdam in a week - 3 days in Paris, 3 days in Amsterdam. You can visit Paris:
1)Disney studios (1 whole day required.Avoid weekends) 2)Eiffel tower top (prebook tickets online.Saves time) 3)Big bus tour (HOHO) Amsterdam: 1)City tour on cycle.
2)Canal Cruise 3)zaanse schans windmill village. Go through the following itineraries for detailed information.
Don't know New year's specifically but here you go. I'm so happy to answer this question for you because I went to exactly those two cities last year! Great on your visa approval. As you might've already searched for Amsterdam itineraries and I'm sure you know the must visits already so I won't talk about the Museums and Red light District. Here are my most favourite ones which are slightly off beat -
1. ADAM Lookout Swing (Highest Swing in all of Europe) - €17,50
2. NDSM Werf - My absolute fav place to chill (Take a free ferry from Amsterdam Centraal) It's a dockyard turned into a cultural centre with a manmade beach of sorts and this awesome cafe called Pllek
3. Vondelpark is an amazing and beautiful place for peace and relaxing.
Do try Poffertjes and Stroopwaffles. I didn't stay much in Paris but a few off beats and lovely places would be 1. Tour Maine-Montparnasse - It's similar to going up Eiffel Tower but in this one you'll have Eiffel Tower in the picture too so even better and cheaper!
2. Petite Ceinture - It's some abandoned railways tracks with beautiful graffiti if you can't find it. 3. You have to try the Crêpes and everything French!
Bon Voyage!