Brasilia, added to the list of UNESCO's list of World Heritage Sites is one of the best examples of a modern and urban architecture city on this list. But not a cozy place as most is on the same UNESCO list ... no trees for a nice shade.
The city is devided in sections of for example banks and hotels etc. so for your idea it has no center.
Most people transport themsleves by car walking seems not done and btw, the distances are immense. By the time weekend comes all people who live in this expensive city escape to other cities like Rio de Janiero or Sao Paulo.

This all was done by three men: Lucio Costa the urban planner, Oscar Niemeyer being an architect and Burle Marx was responsible for landscaping.
The city was built in three years by millions of poor people from the Northeast region. To be honest it wasn't finished by that time but good enough to become the capital of Brazil.

The best place to get your info is at the airport. Friendly English speaking staff and you get a coupon for a discount taxi ride to the city. Open from 7:00 am to 11:00 pm
Besides, all hotel desks have a city map.

Organized Tours

Good walking is crazy here ...
There excists half day tours for about 25 USD. Many hotels which house travel agencies can help you booking such a tour. At the airport it is also possible to book a bus-tour.