The general concept of "downtown" doesn't really have clearly defined borders in St. John's - people just know what they don't consider to be part of it. But the Downtown, as a neighbourhood, is clearly defined.
And it's very small - basically entirely visible (plus most of several other neighbourhoods) in this Bing aerial:
St. John's has just two main downtown streets. Water Street, which is a 3-4 floor strip of brick commercial buildings. It's, in my opinion, a healthy blend of facilities for locals and tourists. For locals, the restaurants, coffee shops, bars, bakeries, and clothing stores are the most popular. We loves our Jumping Bean brews, and drinks at the Grapevine, and and Fog Off clothing. For tourists there are lots of souvenir shops and the like. Antique shops, etc.
Duckworth is much more of a mix. There are stately stone areas (with nicer buildings than Water Street, really, as Duckworth was always more well-to-do and less industrial). Lots of wooden buildings as well. A few stretches of rowhouses behind terraced roads. Duckworth is much more local - bookstores, weird shops, comic stores, theatres, yoga studios, dance studios, and more international restaurants (from Afghan to Indian).
These two streets run lengthwise along the hillside so they're not steep themselves, but are interconnected by many staircases and little streets which also form part of the downtown (for example, the famous George Street - it's really just a back lane for a few portions of Water Street). Most of those are quite steep. Immediately after those two streets the hillside juts up into the rowhouse districts. In some areas, it's literally a cliff face between the two. Many of the ones closest to downtown are quite commercial, and some even look and feel that way, but you're already out of the area purposely built to be a commercial core.
Overall, downtown St. John's is very, very healthy. A fine summer day can see as many people on the street as cities many times our size. George Street and a couple of adjacent blocks of Water maintain a satisfying level of late night vibrancy year-round. There's always lots that can be improved, especially when you live here or visit long enough to notice - but it's in a good place as is too. The main complaint I have is the lack of variety in certain things more common in other cities. Hali87 mentioned Halifax's outdoor patios. There are probably only a half dozen downtown here, most very small. There's none on Water Street at all, just a single row of chairs/tables on the sidewalk outside a handful of cafes. If I want a rooftop bar with a view, there's one outdoor one. If I want a central pedestrian-only courtyard cafe, there's one (well three or four, but all in the same courtyard, so one).