Delhi:  The main city centre station in Delhi is New Delhi, so look for 'New Delhi' as well as 'Delhi'. Delhi Junction station is in central old Delhi. Hazrat Nizamudin and Sarai Rohilla stations are secondary Delhi stations, further from the city centre and best reached by taxi.

Bombay: There are several stations in Bombay, but the most important (and impressive) is the magnificent colonial Victoria Terminus, now renamed 'CST'.  So start by looking for trains from 'Mumbai CST'.  If you don't see any suitable trains, try Bombay Central ('Mumbai BCT') then finally Dadar which is a little way out of the centre.

Calcutta:  The main station in Calcutta is across the river in Howrah, often just shown as 'Howrah'.  Train travel in india from Calcutta to New Jalpaiguri (the railhead for Darjeeling) use Calcutta Sealdah station, often just shown as 'Sealdah'.

Agra:  The main station for fast trains is Agra Cantonment ('AGRA CANTT'), which is an autorickshaw or taxi ride from the Taj Mahal, although Agra Fort is nearer the town centre.

Goa:  The main stations in  Goa are Magdaon and Vasco da Gama, so use these when you check for train times.

The journey from Bombay to Calcutta or from Delhi to Madras is about 36 hours, i.e. typically two nights. On the other hand, travelling on a fast train, Bombay to Delhi or Calcutta to Delhi takes just one night. Amarnath Yatra