45-90 minutes by taxi.
From the international airport
Pre-paid taxis are the recommended way of reaching TIFR from Mumbai's Sahar International Airport. There is a counter just outside the arrival hall. Specify your destination as "Navy Nagar". The rates are posted prominently behind the counter.
You will be given a receipt for your payment. Retain this till the end of your ride; then hand it over to the taxi driver. At the exit from the airport, the police may want to look at this slip.
From the domestic airport
From the Domestic Airport at Santacruz, taxis are not prepaid but charge according to the metered fare. This is converted into the actual fare by multiplying by a fixed factor (currently around 14, after midnight 16.5).
The taxi driver must possess a conversion table for the purpose.
Once you reach Navy Nagar, it is easy to find TIFR. It lies at the far end of Homi Bhabha Road (one of Navy Nagar's principal roads), beyond the Navy Nagar bus terminus, on the left side. Most passersby on the street will know where it is, but remember that it is commonly referred to as "TIFR" rather than "Tata Institute".
From railway stations
20-30 mins by taxi.
Taxis are available from the Chhatrapati Shivaji Terminus. Alternatively, buses (routes 3, 6 Ltd, 136) come to Navy Nagar from outside the local station at VT. TIFR is on the same road as the Navy Nagar bus terminus, which is where you should get off.
From Bombay Central
30-45 mins by taxi.
Taxis are available from the ranks outside the station. Alternatively, you could cross over to the local station and board a Churchgate bound local. You have to buy a separate ticket for the local train. Taxis are available from outside Churchgate. Alternately, a bus (route 137) comes from Churchgate to the Navy Nagar terminus, down the road from TIFR.