Munnar

Rajamalai (Eravikulam) National Park

If possible pick a time based on what attracts you. You will see nature in its full glory during the rainy season with lush green landscape and water gushing down the falls however the probability of meeting the Nilgiri Thar is less as they would not come down as there is no dearth of water.

Pick a slightly drier month if you would like to see the wild goat but the falls may be a bit drier.
We visited the place in 1 week of Aug 2018 and the blooming had not started at all. 
Also you may want to book the tickets online to skip the queue. There is a per day limit to the number of visitors allowed. This is approximately 2500 normally and 3500 during the peak season.

Tea Gardens and Museum:

There are a number of tea estates in Munnar and number of them conduct a tour of the factory for a charge. A couple of them that I am aware of are the Kanan Devan and LockHart. Kanan Devan estae was owned by the Tata group however they sold off their Munnar estates in 2005 and hence the ownership has changed. The Lockhart estate is owned by the Goenkas (Harrison Malyalam). 

Now the tour operators will want to take you to LockHart because of their commissions. The entry fee to Lockhart museum is 200/- while that at Kanan Devan is 90/- per person (somewhere I read 125/-). I have not been to Kanan Devan so no first hand experience but the fee seems to be less. Moreover Lockhart does not allow photography inside the plant. Other than the cost my experience with Lockhart was good.

The guide walked us through the tea processing and also explained the difference in the process of making White, Green and Black tea. 

Please do update your first hand experience.