Traveling around is possible via public transportation. Buses require Rav-Kav, which can be obtained in the airport, or a designated application such as Moovit or Hopon.
Links to prominent transportation tools:
Train: Israel Railways, Moovit, Google maps, Hopon
Bus: Egged, Dan, Nateev Express, Moovit, Google maps, Hopon
Taxi: Gett, Yango
Work-days are Sunday to Thursday. Transportation is limited on Friday from around 14:00-15:00 until Saturday night around 21:00.
Please note that there is no public transportation, i.e., buses and trains, on Saturday (except for in Haifa).
Plane
All international flights arrive and depart from Terminal 3 in Ben Gurion Airport.
From the airport
Train: There is a direct train to Tel-Aviv, including Tel-Aviv University station, Tel-Aviv HaHagana station or Tel-Aviv HaShalom station.
Bus: Alexander Hotel can be reached by taking the train to one of the train stations mentioned above, and taking a bus from there depending on the station and time.
Taxi: There are formal taxi from the airport outside the entrance to Terminal 3 with standard rate.
Recommended: Either a Train to Tel Aviv University station and a taxi from there, or a taxi from the airport.