You can try chikmangloor or wayanad. Both these places have nice treks and plenty of stuff of do. They even have Zostels. So stay will not be a problem. You can also visit Munnar which is not very far from Bangalore. A hidden gem I found was Kotagiri. Such a beautiful place between Conoor and Ooty. You can also check that out.
There are innumerable places that you can explore around Bangalore over the weekends. You can travel to Mysore, Ooty, Coonor, Coorg, Hampi, Gokarna etc. If you're up for some trekking and camping, you can go to explore Tadiandamol, Kumara Parvatha, Kodachadri, Kumta, and other places tucked on the Western Ghats. From Pune, you can travel to Panchgani, Mahabaleshwar, Nashik etc. Since you mentioned that you'll be traveling from Hyderabad, I guess the best option would be to go to Gokarna and chill by the beaches :)
Chikmangalur was where we went last week and loved the place. Coorg is a little hotter during march so you might have that cold feel that you get in the other places. It also depends upon how many days you want to spend. Ooty , conoor, vattakanal, varakala, gokarna, pondicherry are all nice places. If you want to trek then there are some trek groups that go every weekend which you could check out
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