Chelmsford Avenue and Outridge Street which lie on the ridge looking north from Denmark Hill are probably the premier streets in Ipswich. Many big, old houses and beautiful views.
Streets leading up to the ridge are also good, particularly the higher parts of Tiger, Clay, Waghorn, Ellenborough, Nicholas, Quarry, Park and Macalister Streets.
Heading east from Denmark Hill you have the Queens Park/Limestone Park precinct. The streets around the parks on all sides are good, particularly on the higher ground. Best streets include Quarry and Park Streets (which extend from Limestone Park up to Denmark Hill) along with parts of surrounding streets.
Salisbury Road directly to south of Limestone Park and heights of surrounding streets are good and have views to the south/south-west.
Chermside Road and streets directly to the east from Robertson Road in the south to Glebe Road in the north is the best part of Eastern Heights. If you keep going east there are some nice streets in Newtown and Silkstone but you are starting to get into more of the 1960's and 1970's development.
There are some nice spots around Ipswich Girls Grammar but heading north you start getting into flood territory.
The area around Ipswich Boys Grammar, St. Edmund's and St. Mary's is another illustrious part of Ipswich particularly along Woodend Road and streets nearby. This Woodend, Coalfalls area is located in a bend of the Bremer River so again, stick to the hills to avoid flooding.
On the north side of the river, North Ipswich and Brassall have some good spots too but nothing like the others I have mentioned.
The best parts of Ipswich are somewhat like West End and Highgate Hill in Brisbane (if you are familiar with them). The demographics are pretty broad even in the 'best' streets because as soon as you go off the top of the hill you get old houses converted into boarding houses and cheap rentals. Also any area in close proximity to the city and hospital gets a variety of pedestrians passing through... Things are definitely changing with more people doing up old places.