Here are the areas you can spend your day bushwalking in Sydney. Please be careful when you do bushwalking, make sure you bring compass, light colour jacket (easier to be seen from far in case you get lost), water, chocolate bar / food, lotion, bugs repeller and torch.

Berowra Valley

• Berowra to Cowan via Berowra Waters (Time: 6 hrs, Length 12.2 km, Climb: 797 m, Style: one way)
  The view is excellent when you bushwalk explores the ridges and valleys around Berowra Waters and Berowra River area. Especially at Naa Badu Lookout which as a beatiful scenery. You can spend your lunch time around Berowra Waters, in the middle of the walk and if you didn’t bring your lunch, you can grab a bite to eat by taking free car-ferry across the river.
• Berowra to Hornsby (Time: 9 hrs, Length: 19.7 km, Climb: 1,129 km, Style: one way)
  This route is one of the longer formal walks in Berowra Valley Regional Park and this walk mostly follows Berowra Creek along the Great North Walk. You can find an excellent view of the creek around places like Crosslands and Fishponds. Make sure to pace yourself and take regular breaks. Crosslands and Tunks Ridge Reserve are popular rest places.
• Berowra Waters to Cowan Station (Time: 3 hrs 30 mins, Length: 6.7 km, Climb: 573 m, Style: one way)
  The hilly walk has many great views which are great excuses to take rest stops. Take your time to enjoy the views and rock formations along the way as the track leads a nearly direct route o Cowan Station.

Sydney Harbour

• Taronga Zoo to Balmoral Beach (Time: 3 hrs, Length: 6.8 km, Climb: 328 m, Style: one way)
  This walk explores a great section of Sydney Harbour. The walk starts with view of the Opera House and the Sydney Harbour Bridge, and the views continue to get better as you explore bushland and the bays along the way. The walk also explores a historic section of the Harbour, including the fortifications at Bradley’s Head and Chowder Bay.

Botany Bay

• Maroubra to La Perouse (Time: 5 hrs, Length 12.9 km, Climb: 409 m, Style: one way)
  Following the coastline of Botany Bay’s north side, you can have a spectacular view across the South Pacific ocean. It will take you through bushland, past beaches and around 2 golf courses. This track explores all the environments that the north side of Botany Bay has to offer.

Other than those places, Sydney offers a lot of places to have bushwalking such as Blue Mountains, Lane Cove, Norah Head, Ku-Ring-Gai Chase, and Georges River NP or perhaps Manly Dam.