- a day out at Manly Beach. You can walk to other beaches, such as Queenscliff and Harbord. Lots of cafes along the beach to eat at. For something more upmarket, try The Bower or Le Kiosk.
- northern beaches - visit the beautiful northern beaches, and Pittwater. Lunch at Newport Arms (a pub that overlooks Pittwater) or somewhere at Palm Beach.
- walk around the city, esp the Rocks. Weekend market at the Rocks. Pub crawls in the evening. Go to Opera House. Do a bridge climb (book in advance).
- if you want to eat out in more trendy areas, try Paddington, Glebe or Newtown.
- Bondi Beach. Also, walk around Double Bay, which has upmarket, village feel. Go to Watson's Bay and lunch at famous Doyles, or the pub next door. Walk up to the Sydney Heads (entrance from ocean to Sydney Harbour).
- Taronga Zoo, The aquarium, Darling Harbour are other popular tourist destinations.
- Head out to the Blue Mountains. If you wish to stay out there, look at Katoomba or Leura townships. Go to Three Sisters lookout, scenic railway, scenic skyway lots of walks etc. A very historic hotel further up the mountain at Medlow Bath is the Hydro Majestic.
- Other options further out of Sydney...Hunter Valley wine region (2-3 days). Port Stephens area (beaches, good fishing), Southern Highlands (country towns, nice scenery, although more appropriate in the cooler months).
Hope this helps, and enjoy my home town.