What do you call those people who hustle you into restaurants, like those in tourist areas that stand in the street with a menu, suggesting you go into their restaurant. (Brussels is a good example.)
For the theater, these are barkers. These could be called barkers too.
Google, first hit:
barker bark·er /ˈbärkər/ noun INFORMAL
a person who stands in front of a theater, sideshow, etc., and calls out to passersby to attract customers.
One term for the hustler is a tout. The Oxford Dictionaries has this definition
1.1 A person soliciting custom or business, typically in a direct or persistent manner.
The most relevant usage example comes from the verb form:
shop managers would stand in the street touting for business
This may be a British usage.
There are numerous references to restaurant touts in Brussels to be found, such as this one. Some others are in guide books which are not so easy to link.
Evidently, tout as a noun can be an Americanism, too – although it seems to have a different meaning. Maybe we don't have a word for it because we don't see the practice much around here.– J.R. ♦May 22, 2019 at 23:47
@J.R. we say tipster for that, which is also an AmE term. May 22, 2019 at 23:50
An alternative may be promoter. Generally not used within a restaurant context, but a promoter attempts to attract attention from people and get them to visit their establishment (typically a bar/club/etc)