There are plenty of (beautiful) Asian countries that you can travel from India with a low budget. Things get a little expensive only when you turn to Europe and West; but even that could be cost-effective if you're thoughtful in planning.
But first talking about countries you can travel to with a low-budget, Nepal tops that list.
Cozying with the Himalayas, not only Nepal exceptionally beautiful, but it's also quite a cheap travel destination. From accommodation to food to sightseeing -- everything you can do with a limited budget.
(Courtesy: The Jakarta Post)
Following, Bhutan and Sri Lanka fit perfectly on the list. While one is the happiest country in the world preserving some rich culture, other touts serenading beach beauty. Both of them, fortunately, are quite affordable to visit.
Other countries include:
If you can spare more and want to visit Europe, even there you will find a handful of places that you can travel to with a low budget. It includes countries like Poland, Hungary, Romania, Lithuania, Bulgaria, Portugal and Greece.
Now note, these aren’t necessarily the cheap countries. But comparatively, they trade better. They would cost you decent. But if you have planned your trip properly, you can optimize the cost (like booking air tickets at the earliest, avoiding rush season, saying no to luxury suites, more).
There are many places in Africa you can visit too. Not only are they very affordable but they are also the most gifted by nature and history. Cairo, Nairobi, Windhoek, Livingstone, Marrakech, and Kigali.
(Courtesy: The Independent)
I am sure, there are many cities and countries in the world that you can visit with a low budget.
But at the end of the day, again, a lot depends on how you plan your trips.
Hope this answer helps!