Manly surf school does lessons at various locations up the Northern Beaches from Manly itself to Palm Beach (where Home and Away is filmed). Personally I would go for Long Reef for the Aussie surfing experience (remember the beaches will be busy in January).
Also at Palm beach (but on the West side) you can hire boats to pootle around Pittwater for a few hours. You can beach the boats on the little beaches (Mackeral beach etc.) on the edge of the bush, which are only accessible by boat and have a picnic where you feel like a castaway.
If you're outdoorsy there are plenty of places to go bushwalking. Ku-ring-gai national park is pretty spectacular.
Don't pay for harbour cruises, just take the ferry from Circular Quay to Manly instead for the same experience. Manly is great for restaurants and nightlife.
A day trip to the Hunter Valley might be worth it, I would go for small groups that focus on the smaller vineyards personally, unless you want the true backpacker/club 18-30 experience!
Paddington Market on a Saturday morning followed by a wander down the trendier end of Oxford Street is a nice way to spend a Saturday.
The Fish Maket at Piermont is worth a visit. Good for lunch.
The Friday night market in The Rocks makes for a nice wander. Wander over to the other side of Circular Quay for a drink at the Opera Bar.
That's probebly enough!!!!!