Leichhardt Town Hall is on a number of bus routes from central Sydney and from other parts of the city. These include:
370 (Coogee to Leichhardt Marketplace)
438 and 439 (Mortlake to Circular Quay)
440 and M10 (prepay only) (Rozelle to Circular Quay)
445 (Campsie to Balmain)
Downloadable timetables for all these buses are available here.
The closest rail station to Leichhardt is Petersham, about 15-20 minutes walk away.
For car drivers, paid parking is available on Norton Street. Free parking can be found in the vicinity of Pioneer Park on William Street and Henry Street, about 5-10 minutes walk away from the Town Hall.
The Leichhardt Council website has more information on transport in the area here.