Learn English – Word for “lose something temporarily”

To stay one's hunger is perfectly acceptable, and not at all uncommon (though it's actually more likely to be "stay your appetite"). Less common, and with less of a "temporarily" sense, would be assuage one's hunger. But I think probably the most common idiomatic usage is...

Here - have a sandwich to stave off your hunger until dinnertime.

...which my mother used to say to me when I was a child. Perhaps this one gains traction by alliteration / association with both stay and starve.

to stave off
to fend off, to ward off (something adverse) _{Merriam-Webster}

(To metaphorically repel / drive away using a stave = staff = stick.)

You're right in that metropolis may not be the ideal choice here. Below are a few ideas, not all of which is a single word:

"Welcome to your (ultimate)..."

• hub
• one-stop shop
• all-in-one destination
• mecca