Los Angeles is unique in this regard, as its center was largely undesirable and lay fallow for decades, as wealth traveled west, into the hills, and into distant suburban nodes. Downtown Los Angeles was (and largely is) surrounded by poor Latino neighborhoods, like South Central, Northeast LA, and East LA proper. Only recently has DTLA become a place people actually want to live and hang out - and has been developing rapidly, I should add. Owing to this recent development, there has been little spillover from DTLA into the surrounding SFH areas, although some has trickled into the nearby multifamily areas, such as Koreatown, and increasingly, Westlake.
IMO, the closest affordable SFH area would be the Historic South Central neighborhood, a large area just south of the 10 freeway and east of the 110 freeway, and largely characterized by early 1890s-1920s Craftsman and Victorian bungalows. It is a pretty poor, almost entirely Mexican (with a few black old-timers hanging around), and has literally no gentrification to speak of. Houses here, despite being right next to DTLA, are vastly cheaper than a comparable in-town neighborhood in NYC, Boston, DC, San Francisco, Chicago, etc., would be. Funny enough, people think of South Central as an all black neighborhood (really, a region), when in reality is is probably easily pushing 70% Hispanic, and 100% Hispanic in the areas east of the 110, such as the Historic South Central neighborhood.
https://www.google.no/maps/@34.01940...!6m1!1e1?hl=en
https://www.google.no/maps/place/Los...!6m1!1e1?hl=en
https://www.google.no/maps/place/Los...!6m1!1e1?hl=en
Boyle Heights and Lincoln Heights (and also El Sereno and City Terrace...as mentioned, LA's downtown is surrounded by some of the poorest and roughest areas of the city), which lay to the east and northeast of Downtown, are also mostly SFH and still affordable, although there has been small-scale gentrification in both. Many young, college-educated, white first-time buyers are looking in these areas, as some of the options from the previous decade (Echo Park and Highland Park, mostly) have gentrified and gotten fairly pricey. Lincoln Heights will probably gentrify faster than Boyle Heights, where there has been substantial, organized Chicano (Mexican-American) pushback and opposition to gentrification, including literal harassment, intimidation, and threats of violence towards newcomers and real estate agents.
Lincoln Heights:
https://www.google.no/maps/@34.07197...!6m1!1e1?hl=en
Boyle Heights:
https://www.google.no/maps/@34.04045...!6m1!1e1?hl=en
https://www.google.no/maps/@34.03969...!6m1!1e1?hl=en
Oslo follows a more typical European model, where areas close to the center are desired and sought after, as demand for inner-city living is quite high in what is one of, if not, the fastest-growing capitals in Europe. Historically, there has been an east-west split, with the areas west of sentrum (center) being posh, urbane and generally well-off. Those to the east have historically been poorer, more industrial, and as of late, the center of Oslo's large immigrant population, which is a just over 1/3 of the city's overall population. Grønland and Tøyen, just east and northeast of the sentrum (5 minutes walking to the first, 5 minutes by train to the other) were traditionally the poorest, most immigrant areas in the inner-city, but things are starting to change as newer, wealthier homeowners and the businesses they attract move into such areas. Gamlebyen, which is just behind the main train station, and Vålerenga/Galgeberg which are a little more distant, are my guesses for the most affordable areas in (relatively) central Oslo. The first area is an 1890s tenement flat area of mostly lower middle class white Norwegian families, and has a strange rockabilly/50s vibe. The other two are more working class, and are primarily defined by more small-scale 1800s SFH's, occasionally punctuated by tenement blocks from the 40s/50s.
Gamlebyen:
https://www.google.no/maps/@59.90767...!6m1!1e1?hl=en
Vålerenga:
https://www.google.no/maps/@59.90835...8i6656!6m1!1e1
Galgeberg:
https://www.google.no/maps/place/Osl...!6m1!1e1?hl=en