It depends what is your definition of romantic.
Is it a big wellnes Hotel with all the luxury or is it a more simple place where you can make little walks and enjoy the cold and clear air. Hear the sizzling noise that your shoe make in the snow. Or just sitting in the sun an feel the warm. (For Indian maybe difficult to understand what is so nice about sitting in the sun. But you will soon when experience how cold is in the shadow).
St. Moritz is a little city with all the disadvantage. It has a lot of traffic and surrounded by very rich you feel poor when you are only rich. You will feel not so much of it as long your are in a Hotel with the big names like Kulm or Palace. But to be honest for that experience you don't need to travel around the half world. If you like the this part of the Engadine I suggest more Pontresina that is a little more charming then St Moriz but still big enough to have all it needs and with some nice ***** Hotels.
A bit more traditional is Scuol in a other part of the Engadine. Also in a similar style is Bergün which spezial famous for sledge slide. You can rent the sledge there and it don't need years of learning like skiing. The last town in Graubünden I would like to mention is Vals . The town it self is not very beautiful but the Thermen a hot spring bath is nicest I know. So if stay in one of the towns I mentioned before it is easy to make a little detour on your way back to Zürich Airport.
My personal favourite is Albinen in the Valais a complete different part of Switzerland. The problem is if you want to make day trips you have to go every time down to the valley and come back before the last post bus and the other disadvantage is there are no luxury hotels. So it is a good place if you just want to have it nice and quiet. But you have still the possibility to make day trips to the spa of Leukerbad and to Zermatt to see the Matterhorn.
Sorry the more or less double post but did some wrong click.
