Take the Manly Ferry. This is the best and cheapest way to see the harbour. Manly itself has the best beaches.
Yes, take the ferry, departing about every 30 minutes during the day, but don't buy a cash ticket ($6.60 single from 18th April) buy a My Multi3 Day ticket or even better the My Multi1 weekly ticket and travel around on all ferries, buses and trains too. Much better to let someone else do the driving in Sydney!