Karnataka Tourism places Kalhattigiri ten kilometres from Kemmanagundi, which makes the two a natural pair. The distance is short, but the hill road and changing weather mean the day should be planned around daylight rather than a packed checklist.
Falls first in uncertain weather
If rain is building, see Kalhattigiri while the lower road is still comfortable and decide at the site whether wet rock allows a close approach. The temple is the fixed point of the visit even when flow is weak.
Hill station second
Continue to Kemmanagundi for its gardens and a viewpoint only if visibility and time allow. Do not add a long trail late in the day merely because the falls stop was brief.
Leave a descent margin
Fuel and broader services are easier on the plain. Start down before dark, especially after rain, and keep an alternate plan for mist that removes the value of the upper viewpoints.