The primary mode of public transport within cities in Tamil Nadu is:

Metro Rail
Local Trains
Buses (Government & Private)
Taxis

The primary mode of public transport within cities in Tamil Nadu is buses (Government & Private).

Buses are the most common mode of public transport in Tamil Nadu, accounting for over 60% of all trips. They are operated by both the government and private companies. Government buses are generally cheaper than private buses, but they are also more crowded and less reliable. Private buses are more expensive, but they are also more comfortable and reliable.

Metro rail is a relatively new mode of public transport in Tamil Nadu. The first metro rail system was opened in Chennai in 2011. Metro rail is a fast and efficient mode of transport, but it is also expensive. It is not yet available in all cities in Tamil Nadu.

Local trains are another mode of public transport in Tamil Nadu. They are operated by the Indian Railways. Local trains are a fast and efficient mode of transport, but they are also crowded and less comfortable than buses. They are not available in all cities in Tamil Nadu.

Taxis are a private mode of transport in Tamil Nadu. They are available in all cities in Tamil Nadu. Taxis are a convenient and comfortable mode of transport, but they are also expensive.

In conclusion, the primary mode of public transport within cities in Tamil Nadu is buses (Government & Private).