Just behind the Catedral Basilica, you'll find this tram that will take you down to the lower town. I believe it was 1.50 reais and it takes about 3 minutes, so it definitely beats walking. However, it doesn't beat the Elevator Lacerdo which is even cheaper and provides better views.
***update*** oops, thanks to VTer Kittlelite who told me that the Plano Inclinado costs the same as the Elevator Lacerdo at the bargain of only 5 centavos!! Thanks, Kittlelite!