It's depends on,how you want to enjoy your trip.. there are so many places in India like,
Andaman
Ooty
Hampy
Lonavala
Pondicheri
Goa
Dalhousie
Mcleodganj
Manali
Kasol-Tosh
Ranikhet
Nainital
Shimla
Derahdun-Mussouri-Auli
Haridwar-Rishikesh
Sikkim
Arunachal
Meghalaya.. 15k will be a standard budget to visit anywhere in India.
Hey Monica, Within your budget you can go ahead for these Places in India ... Please see that within 15k, the transport charges to and fro to these places are not included ... And you can calmly book your room and also spend for food and small souvenir back home within your budget .... Varkala in Kerala Pondicherry in Tamil nadu Hampi in Karnataka Coorg in Karnataka Rishikesh and haridwar in uttarakhand Varanasi in Uttar Pradesh Happy Travelling !!!
Munnar in Kerala is a budget friendly place to experience in December-January. The climate is the best at the time and you can do a lot of activities like site seeing, trekking. The place has a lot of tea plantation, reserve forests, beautiful villages, reservoirs and the views are absolutely mind blowing. You'll get good hotels here and you won't regret the visit. Check it out
With a 15 k budget you can try beautiful destinations in North Bengal & Sikkim. The weather is spectacular during this time of the year at these places.
Himachal Pradesh is best place to travel during the winters if you're fond of snow. Also Rajasthan is also a good choice with many places to choose from like Udaipur, Jaipur, Jodhpur, Jaisalmer, Mount Abu etc.