The usage of the mixed script (Hanja with Hangul) was commonplace during most of the twentieth century. Most books, articles and newspaper employed the mixed script, and in the earliest stages of mixed script writing show a form of language that is alien and not readily comprehensible without previous studies. For example, the opening lines of the "Declaration of Independence of 1919":
吾等(오등)은 玆(자)에 我(아) 朝鮮(조선)의 獨立國(독립국)임과 朝鮮人(조선인)의 自主民(자주민)임을 宣言(선언)하노라. 此(차)로써 世界萬邦(세계 만방)에 告(고)하야 人類平等(인류 평등)의 大義(대의)를 克明(극명)하며, 此(차)로써 子孫萬代(자손만대)에 誥(고)하야 民族自存(민족 자존)의 正權(정권)을 永有(영유)케 하노라.
The "grammatical" words like 吾等(we), 玆(hereby), 我(we/our), 此(this) are remnants of Classical Chinese literary tradition. These fell out of use soon, and while some words like 告(declare) survived somewhat longer but still they fell out. The usage of Hanja became restricted to the words that are Sino-Korean that are not readily replaceable with the native words without damaging idiomaticity, and the Hanja usage continued in this somewhat moderated form. The same text written in 1970s may read as this: (this is not a real text, but my version)
우리는 이에 우리 朝鮮(조선)의 獨立國(독립국)임과 朝鮮人(조선인)의 自主民(자주민)임을 宣言(선언)하노라. 이로서 世界萬邦(세계 만방)에 告(고)하야 人類平等(인류 평등)의 大義(대의)를 克明(극명)하며, 이로서 子孫萬代(자손만대)에 誥(고)하야 民族自存(민족 자존)의 正權(정권)을 永有(영유)케 하노라.
More subsequent changes were made in order to bring the spoken and written language closer. As a result, a large number of Sino-Korean words actually dropped out of usage over time, and the native words were replaced where they sound more natural in the spoken language. A modernised version would be: (again, my version)
우리는 이에 우리 朝鮮(조선)의 獨立國(독립국)임과 朝鮮人(조선인)의 自主民(자주민)임을 宣言(선언)한다. 이로서 世界(세계) 모든 나라에 알려 人類平等(인류평등)의 大義(대의)를 밝게 드러내고, 이로서 後代(후대)에 전하여 民族自存(민족 자존)의 正權(정권)을 永遠(영원)히 갖게 한다.
You would notice a number of words replaced. 萬邦 or 克明 are not commonplace words and hence dropped out, while 人類 or 正權 is and remains. 永有 is archaic, and it has been paraphrased as "영원히 가지다" instead. A text printed in the recent two decades or so may contain this much Hanja, but it wold be exception (such as scholarly texts) rather than norm. Contemporary works may contain no Hanja at all or only occasionally for disambiguation purposes. Sometimes they may include a fair number of them (fairly common in historical novels, for example) but they would all be glossed with Hangul. Referring back to the original post, the signs of the Chinese restaurants are written in Chinese because they're Chinese restaurants and it is an exception rather than a norm. They would generally have Hangul name somewhere (interior, a small print on the sign, menu, etc..) so the Hanja-illiterates can remember their name.
The only field I know to employ an extensive amount of Hanja is - well, not surprisingly - law. There are proponents of Hanja education who claim that a solid knowledge of Hanja helps the students with the understanding of the principles of word formation, but they are not without critics. The extent to which Hanja should be taught (and, should be "known") is a major topic for debate, and I wouldn't claim a position here. The previous claims that the modern readers can't read the classics (both Chinese and Sino-Korean) without the knowledge of Hanja weakened significantly since the blooming translation industry from Sino-Korean/Hanmun to Modern Korean.
For those who are curious about the contents, this is the translation:
We hereby declare the independence of Korea and the soverignty of the Korean people. We hereby announce to the all nations in the World to make the great justice of human equality known, and transmit this to the subsequent generations so they may possess the soverign national polity for the eternity.