You can go for a low budget trek like
1. churdhar trek,sirmor district, Himachal Pradesh
2. bhramtal trek,lohajung, uttrakhand (Basically a winter trek)
and if you are a highly adventures person then you can go for
3. chadar trek,zanskar vally,leh
I would suggest you to visit hill stations in Tamil Nadu which is budget-friendly as well as worth visiting for a blissful holiday.
These could be reached by flight or train to Coimbatore and take a bus or car journey for 1-1:30 hours and is very economical.
For these, you have to reach Salem(Tamil Nadu) and then take a bus or car journey for 1-1:30 hours.
Take a flight to Bangalore /Mysore(nearest airport) and then take a bus to Coorg.
Best part is consider taking a homestay which is cheaper than hotels and you will be able to spend time with the native people and taste their delicious foods.
It depends on which part of India you are located because based on the distance, you can plan your budget and travelling. Hope below suggested places might help you :)
Towards - South India - Coorg
- Valparai - Andaman
- Lakshadweep Towards - North India
- Sonamarg - Srinagar
- Gulmarg - Manali
- Rajasthan(Jaipur, Jodhpur, Jaisalmer, Udaipur)
- Nainital - Mussoorie