Hi Yoshita,
For the Cheapest travel destinations from india for a family vacation you can explore Asia:
1) Srilanka
2) Nepal
3) Bhutan
4) Thailand
5) Singapore
6) Indonesia
9) Sechelles - If you love Island no visa is require for here and its very pretty.
Hi Yoshita, Trip budget mostly depends upon the no. of days in travel plan, stay type, food and exploration/activities. There are so many great international destinations near India where you can easily go with your family. Checkout below destinations along with an average cost for a person (mid-range traveller) for single day in that country.
1. Bhutan - Rs 5,000 approx.
2. Nepal - Rs 1,800 approx.
3. Myanmar - Rs 4,200 approx.
4. Vietnam - Rs 2,800 approx.
5. Bali - Rs 4,200 approx.
6. Malaysia - Rs 5,500 approx.
7. Sri Lanka - Rs 2,900 approx. You can checkout some great stay options here: https://www.tripoto.com/hotels. Happy travelling!