Take this road if you are heading towards Thekkady, Kumily or Chinnakanal are south of Munnar
This highway is 4 or 6 lanes most of the way.
[#road]Bangalore → 40km → Hosur → 50km → Krishnagiri → 110km → Salem → 93km → Karur → 74km → Dindigul → 58km → Periyakulam → 16km → Theni → 16km → Bodinayakanur → 50km → Munnar
Of the 510km total distance from Bangalore to Munnar, you'll be on the NH44 & NH544 well over 350km.
What this means is though its a longish route, you could cover the distances quite fast compared to the other other two road options (see Bangalore to Munnar via Salem and Bangalore to Munnar via Chamarajanagar), thanks to the 4 lane highway.
From Dindigul, take the right diversion to NH45 towards Theni. This too is an excellent highway compared to NH44. At Theni, take the diversion for NH183. The last 60km after Bodinayakanur, the road winds through the plantations and ghat sections, and slower too.
Alternatively after Karur you can leave exit NH44 at Aravakurichi and head for Dharapuram. From Dharapuram head to Udumalpet and then to Munnar via Marayoor.
The Aravakurichi to Udumalpet route, though 2 lane is reasonably good to drive.
Bangalore to Munnar Road Route Map