There are numerous places to visit in Karnataka during the march. Some of them are Banglore, you can enjoy a nightlife here, Mysore, Coorg (known for its scenic natural beauty), Manglore( for its clean beaches), Nilgiris sanctuary etc.
Visit Hampi if you love history and architecture.
If you want mountains, Coorg should be your choice. But if you want a peaceful little place with mountains and beaches, go to Gokarna.
Hey, In Karnataka, since March being the start of summer, you'd want to avoid the hotter places. Try Chikmagalur, Shimogga, Mysore, Kodagu and Coastal region (Mangalore, Udupi, Gokarna) Dandeli is also a great option.
Avoid places in North Karnataka due to scorching heat during March. you can try visiting places like Coorg, Chikmagalur, Sakleshpura, Mysore and Shimoga.