I can give you a run down of the universties in New South Wales.
Uni of NSW:
My own alma mater (mechanical engineering). Strong engineering university with good links to industry. In Sydney's eastern suburbs so you will be near the beach and the CBD, but be ready to pay some serious rent in the housing in that area, it ain't cheap!
Sydney is Australia's largest and oldest city with over 4 million people. Plenty to see and do all year around.
BTW, I noticed you didn't have University of Sydney on your list. This is Australia's oldest uni and the main "rival" to UNSW. Located in Sydney's inner west a few kilometres from the CBD.
Uni of Newcastle:
Newcastle is 2 hours drive north of Sydney on the Central Coast. It used to be the major "steel city" in the area before they shut down the factories. As a result the whole place has now been cleaned up and is regarded as a great place to live. Newcastle uni has a good chemical engineering reputation.
You will be close to beaches and all the facilities of a city, but you will have more of a "regional Australia" experience than Sydney. If you like more of an active night life such as bars and clubs then Sydney is probably a better option.
University of Wollongong:
1 hour south of Sydney, right on the coast. Wollongong is basically Newcastle's sister city. Another "steel city", but the uni is at the "nice" end of town, away from the steel industry.
Hope this helps,