The suburb name isn’t provided in the GTFS data. You could do your own intersection with the provided stop coordinates and suburb / locality boundaries from PSMA.
There is also the TXC dataset, which does provide a suburb / locality name in <Suburb>… but stops don’t necessarily match 1:1 with the GTFS data. e.g.:
<StopPoint CreationDateTime="2016-04-07T00:00:00">
<AtcoCode>000000207233</AtcoCode>
<PrivateCode>207233</PrivateCode>
<Descriptor>
<CommonName>Ryde Rd at Minnamurra Ave</CommonName>
</Descriptor>
<AlternativeDescriptors>
<Descriptor CreationDateTime="1900-01-01T00:00:00">
<CommonName>10113895</CommonName>
</Descriptor>
</AlternativeDescriptors>
<Place>
<NptgLocalityRef>ES000000</NptgLocalityRef>
<Suburb>Gordon</Suburb>
<Location>
<Longitude>151.140303</Longitude>
<Latitude>-33.754955</Latitude>
</Location>
</Place>
<StopClassification>
<StopType>BCS</StopType>
<OffStreet>
<BusAndCoach>
<Bay>
<TimingStatus>otherPoint</TimingStatus>
</Bay>
</BusAndCoach>
</OffStreet>
</StopClassification>
<AdministrativeAreaRef>000</AdministrativeAreaRef>
<Notes>Ryde Rd at Minnamurra Ave</Notes>
</StopPoint>