Newtown is an eclectic bohemian part of Sydney, a place where expensive restaurants and designer clothes stores can sit adjacent to 2 Dollar Shops and second hand bookstores. Newtown is one of the best places to go people watching as the demographic of people who frequent the area is highly diverse and consistently outrageous and weird. An "artsy" current runs throughout the suburb; there are several murals painted on the sides of buildings, including an iconic "I have a dream" piece of street art featuring Martin Luther King, J.R.. Most of the architecture in Newtown (as in much of Sydney) is Terraced housing, but there are also several beautiful old buildings, including the Newtown Post Office.
As Newtown is within walking distance of The University of Sydney there is a strong student population in the suburb. College drinking night is Wednesday, so this is the best night to experience drunk Sydney Uni student culture in Newtown (and who wouldn't want to?!), starting at the Marlborough Hotel (colloquially called "The Marly"). A much needed kebab after this experience can be located at "Aidan's" across from The Marly, or at "Istanbul" further west on King Street.
The best burgers in Newtown can be tasted at New Zealand owned "Burger Fuel", and a cheap Asian meal can be obtained at lunch time at one of King Street's many Thai, Vietnamese or Japanese Restaurants.
Best coffee in Newtown is a highly debatable topic, but Campos coffee house probably has the unofficial title.