If you are not planning on spending much time in the city itself, then I recommend staying in one of the hotels near Sydney. The following hotels are located in the Northern Beaches area and the Hunter Valley.
Accommodation in Sydney is diverse and suits all budgets. You will find plenty of hostels, Air BnB accommodation as well as good hotels. The following two hotels are highly recommended for solo travel and are reasonably priced.
Unless you are keen to unpack your suitcase just once on your trip, it might be worth considering more than one hotel to explore different areas.
Manly is a popular beach suburb on the Northern peninsula. It is in an idyllic location opposite the stunning Manly beach. Shops and restaurants are within a short walk and it is a safe area to walk around in. The hotel offers studio apartments as well as regular rooms.
Pokolbin Village is a 40 acre resort and an ideal place to stay if you are travelling by yourself in the Hunter Valley. If you are signing up to a wine tasting tour, they will pick you up and return you to the hotel. Guests can use the pool and barbecue facilities. A shuttle bus will take you to and from the nearby restaurant at night.