Ooty and Munnar are 2dffrent kinds of places if you are looking for peace and if you want to find yourself visit Munnar untouched area's but if you are looking to have just chill out thn Ooty.
I'm near ooty there are lot things to explore here, steam engine trains , mukkurthi national park, avalanche reservoir which is comparatively gives nice views like idduki dam , and some viewpoints and falls...But nowadays there is heavy traffic seen you Will often feel tired or irritated.... weekdays are preferable compared to weekend... however munnar is a peaceful place compared overall to ooty as ooty is crowed area,you can't feel the nature at the fullest.... you should travel at the borders of nilgiris like kotagiri, manjoor, mudumalai,avalanchi, emerald like area's to see the real beauty of Blue mountain (Nilgiris)
Neither Ooty, nor Munnar. Travel to Kotagiri near Ooty and Valparai near Munnar. These are less traveled places and are more beautiful. Hotels are cheap as well.