Greetings from Sydney!
Sydney in April, experiences fairly warm weather, you can still check out the beaches, bushwalks, harbour scenery and all outdoor attractions. Generally, theres not much rain during April either, so it's a good time to visit. There can be a few cooler days, but on the whole, you should be pretty happy with the weather.
Be sure to check out the Blue Mountains, its a 2 hour train from downtown Sydney. There's loads of things to do and see if you're happy to jump on a bus, ferry or train and escape the bussle of the downtown area.
Check out NSW Holidays & Accommodation, Things to Do, Attractions and Events for (www.visitnsw.com) for some local things to see and do.
Whatever the weather, we recommend staying at the Marriott at Circular Quay, which is where most cruises dock. It's about a block walk, and very convenient to the Opera House and the ferries to the zoo and other waterside attractions. The hotel is very nice, and gives you a great place to recover jet lag before embarking on your cruise.