Let us go for a picnic to Courtallam.

  1. Let us go on a picnic to Courtallam.
  2. Let us go to Courtallam on a picnic.
    Are both sentences fine?

Better to say: for a picnic.

  1. Let us go to Courtallam for a picnic.
  2. People are calling this place the Spa of South India.
  3. In June & July people from other parts of our country are rushing here to bath and rest.
    Are all these sentences OK

‘to bathe’ (swim).

Alan,
In Courtallam falls people are taking shower only.
It is not a pond or a lake to swim.
So my word ‘bath’ is OK? or still I have to use ‘bathe’?
Please clarify me. Thanks.

It’s still ‘bathe’ rather than ‘bath’, but given the information you have provided, I would not use it. I would simply say ‘shower’.