Determining which neighborhood is Austin’s smallest is more difficult than one might think. The biggest issue is not finding the stats (though that’s kind of difficult too), nor determining boundaries. Rather, it’s deciding what constitutes a neighborhood.
The city of Austin has its planning areas, which often combine two or more neighborhoods; the Austin Neighborhoods Council has many more, as it counts any area with a neighborhood or homeowners association (and a homeless neighborhood association as well); real estate professionals use their own map, based on its Multiple Listings Service; all of them overlap to some extent.
Most important, though, seems to be a sort of historic/cultural approach—how a neighborhood has been defined, and named, historically—coupled with how its inhabitants identify it and how it’s perceived today.
Measuring 40 acres, however, Swede Hill is indubitably small and it meets most the criteria above (it’s combined with surrounding neighborhoods into the Central East Austin city planning area for that). Originally developed in the 1870s by Swedish immigrants who built homes near their downtown businesses; when the area had grown to sixty-seven such families, it became known as Svenska Kullen (Swedish Hill) and is now known more familiarly as Swede Hill.
Originally bounded by Waller Street on the east, Red River Street on the west, 15th Street on the south, and 19th Street (now Martin Luther King Jr. Boulevard) on the north; the construction of IH-35, the University of Texas' Frank Erwin Center, and general urban development decreased its size of dramatically and moved its boundary to the east in the 1980s. In 1986, an even smaller portion of the neighborhood—a few blocks on East 14th and East 15th streets between Olander and Waller streets—was designated and added to the National Register of Historic Places "on the basis of the intactness and cohesiveness of the residential structures," according to its nomination.
Swede Hill has managed to stay overwhelming residential, due in part to an active neighborhood association as well as its diminutive size. There are even fewer residences than the size of its boundaries might indicate, due to the often-overlooked presence of the historic Oakwood Cemetery—the oldest one owned by the city—on a fair percentage of its northeastern border. It also has a lovely pocket park and an underdeveloped swath of commercial lots on East 12th Street, its southern border.
The already popular neighborhood has seen an influx of residents in the past few decades as the city has grown and East Austin in particular has been be transformed, and it hasn't been able to suppress completely the inevitable McMansioning that follows. Its southern edge, too, will at some point see commercial development. For now, though, it remains a green, low-key spot full of mostly small-scale, older homes and many residents committed to keeping it that way.