このofはなんですか？

私の日本語は様々な誤るところがあってごめんなさい。

この例は、どのような"local restaurant"を特定する語句の"of their choosing"を「主要部」は"of"です。
"of" is the 'head' (primary member) of the phrase "of their choosing", which modifies "a local restaurant".


"of their choosing"は、"a local restaurant"に"of"を使って付けられます。
"of" is the word that attaches "of their choosing" to "a local restaurant".

このように"of"を使う文法形式はあまり通常ではないですが、時々一番自然的です。
It is not very common for "of" to modify nouns in this way.


It is much more common in Romance languages such as French ("of" = "de")
"un restaurant _de_ leur choix" ~ "a restaurant of their choosing"
"un trou _de_ cinq mètres _de_ profondeur" ~ "a 5-meter hole / a hole that is 5 meters deep" (no "of" in the English version)


構成
patronize [a local restaurant [of their choosing]]