Visitors to Newcastle will find a variety of day trips they can embark on.
Probably the best way is to travel by car so you can stop at any spot that takes your fancy. Rent a car that suits you and if you're not used to driving the Australian way, follow a few driving rules and you should be okay.
If you prefer not to drive, there are bus tours available, or you could take the train, where available, and go on from there.
Westward or Northward
Probably a day trip of choice because of its proximity to Newcastle is a tour of the Hunter Valley wine country. Newcastle is, in fact, in the Hunter region and the Valley is less than two hours away west-northwest of Newcastle. Take the Pacific Highway out of Newcastle and watch for turn-off signs to Cessnock or Pokolbin in the heart of wine country. Get a map of the wineries in the area so you know where to go.
Closer to Newcastle is Port Stephens which should be very much less than an hour away traveling northeast through Williamstown and Anna Bay to Nelson Bay. There are various cruises you can take at Nelson Bay such as dolphin cruises or across the water to Hawks Nest and Tea Gardens. Or you can simply laze away the day on the area's beaches, or try waterskiing or windsurfing.
Farther north is Port Macquarie, another holiday destination on the New South Wales North Coast. The area is of particular attraction to lovers of water sports and leisure activities. Around two and a half hours by road from Newcastle.
Or Southward to Sydney
If you prefer to travel south, The Entrance and Terrigal on the New South Wales Central Coast are just about an hour away, or you could take an extra hour and go on down to Sydney, and spend a day of city sightseeing from The Rocks to the Opera House, through the Royal Botanic Gardens, The Domain, Hyde Park, and on perhaps to Darling Harbour.
The red Explorer Bus -- best to take it at the Visitor Centre in The Rocks, if you're not too familiar with Sydney -- is, for many, a favored option, since you can get off any number of times at any point along its route and get back on when you're ready to do so.
Your day trip choices are many and varied and much depends on what interest you. Visit the Newcastle visitor center to find out what your choices are.