Tip : I have visited ooty as a solo lady traveller and it's one of the safe places to visit, but obviously you need to take safety measures and be responsible. There are local sightseeing buses from ooty to visit all the above places. You can go for trekking and bike rides as well. I stayed at Serinity Inn Hotel in charring cross at ooty, the caretakers and the owners were really warm and made me feel safe.
That's all folks, keep exploring and keep smiling.