Trieste "Ronchi dei Legionari" airport is about 25km north-west of Trieste. From there you can take the APT coach service to the centre of Trieste - Line 51, tickets are available from the blue machine just beyond the arrivals gate (APT timetable). (Note that this service runs much less frequently at weekends. Tickets can be purchased also downtown from the bus station next to Trieste Centrale).
A good option, especially at weekends, is to book a seat on the "Science Bus" which is a shuttle service between Trieste and all the nearest major airports - Ronchi, Treviso, Marco Polo and Brnik (Ljubliana). Be sure to book your seat on the Science bus at least two days before you need to use it and ask us for a voucher code for when you book online.
As a last resort, take a taxi: the cost is around 50€.
The Venice Airports(Marco Polo and Treviso) are another option for coming to Trieste. From there you'll need to take the coach service (tickets available from the ATVO service desk at the airport foyer) to Venezia Mestre train station and continue on with the train to Trieste Centrale (around one and a half to two hours).
The main train station is Trieste Centrale, about 5km from SISSA. You'll need to take the 38 bus from Piazza Oberdan (see below) or a taxi. Note that most long distance trains coming to Trieste pass through Venezia Mestre train station, which might involve changing trains at Mestre. In Italy, train tickets should be purchased in advance either from an automatic vending machine or from a sales assistant. Validate your ticket using the machine nearby the tracks before travelling.
SISSA is very close by the Obelisc, just outside Opicina, as shown on the map. When arriving at SISSA, drive through the main gate and then press the buzzer to be allowed through the barrier, and drive down taking a right turn into to the underground car park.
Shuttle Service SISSA&ICTP
A shuttle service between ICTP and SISSA is available with the schedule shown here.
Take the 38 bus from via Galatti (opposite the Birreria Forst) next to Piazza Oberdan (every 20 minutes in the morning rush hour, every half an hour in the evening). Get off the bus at the last stop, right outside the main SISSA gate. Tickets are available from news kiosks: You can buy a single ticket, a carnet of 10 tickets or a monthly pass. Validate your ticket once on board the bus. Takes about 15 minutes.
You can get to SISSA also by the historical tram line Trieste-Villa Opicina (http://www.tramdeopcina.it). The tram leaves every 20 minutes from the downtown terminus in Piazza Oberdan (close to 38 bus stop). To arrive to SISSA, get off at the Obelisco stop (a 20 minutes journey). From the Obelisco, walk down Via Bonomea for about 10 minutes. It is a real picturesque experience!