Sure, I can provide some travel tips for your visit to Chennai, Ooty, Coimbatore, and Madurai:

Best Time to Visit:
The ideal time to visit these destinations in Tamil Nadu is from October to March. The weather is pleasant which makes sightseeing and outdoor activities more enjoyable.

Route and Accessibility:
Chennai is well-connected by air, rail, and road. From Chennai, you can head to Coimbatore which has an airport and several trains running from Chennai. From Coimbatore, Ooty is just a short drive away. Cars and buses are available for this journey. You can then travel to Madurai from Coimbatore via NH 44.

Altitude and Acclimatization:
While Chennai, Coimbatore, and Madurai are located at lower altitudes, Ooty is a hill station at around 2,240 m. While altitude sickness is not common here, it is advisable to relax and reduce any physical activity for the first few hours to adjust to the cooler temperatures.

Accommodation and Booking:
It is recommended to book your accommodation in advance to avoid last-minute hassles. All four locations have a range of accommodations options to choose from, including budget, mid-range, and luxury hotels.

Clothing and Essentials:
Pack summer clothes for Chennai, Coimbatore, and Madurai. These cities can get hot during the day. However, Ooty has a colder climate so packing light woollens including jackets and shawls is advisable.

Health and Safety:
Carry sunscreen, hats, and sunglasses for protection against the sun. Also, carry any necessary medications. Stay hydrated, eat healthy food and be careful while doing activities like trekking in Ooty.

Local Etiquette and Respect:
Respect the local culture and traditions. When visiting temples, dress modestly and take off your shoes before entering. In Ooty, respect the environmental norms and avoid littering in the hill station.