I can't answer whether this would work for the rest of the network, so I'll focus on Arqade specifically.
Questions on Arqade are meant to solve problems, so in general, I would hesitate putting non-problems (puzzles/challenges) on the main site. We do have a game-identification tag, but in pretty much every instance, we are solving an actual problem; the OP does not know what the game is. For example:
Also note that compilation-style puzzles (multiple cropped images compiled into a single identification challenge) were deemed off-topic for the main site.
Thus, I don't think it would be a good idea to hold puzzle/challenges on the main site.
We have used meta for community-level events before. We've organised community game servers, held movie nights, game nights, and tournaments. More recently, we've been hosting a Screenshot of the Week competition which has seen good community support.
We've also been soliciting ideas for these sorts of things, so ideas like yours are welcome:
The problem that I see with hosting your challenge on Meta regularly, is that (as currently described), it sounds like the sort of thing that will attract lots of new meta posts. I don't think we want or need 20+ active 'Where am I?" challenges drowning out actual, pertinent community discussions.
If you were to flesh out the rules of your challenge more fully, altering them slightly so that it could be run out of a single meta post every week or month etc, then it would work for us. Otherwise, it may be more suited to another space (perhaps even in chat?)