Federal Park is a 24h off-lead dog park in Annandale. Dogs are also allowed on the sportsfields except during the games (which would probably be fun for the dogs, not so much for the players). Lot of facilities are around the park and also one of the best dog friendly pubs, The Annandale, is not too far.
Glebe Foreshore offers great walks either along the canal (where your dog can remain off the lead most of the time) OR on the actual Foreshore all the way up to the small dog beach Blackwattle Bay Park.
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