The city with the weakest production?
While I kind of understand your logic there, I think its not sensible to do that. You'll have to invest more turns there in getting the Ironworks built in the first place, then once it is you'll be getting less benefit from it, given that its +50% of a smaller number.
If you have a low production city that needs picking up, I'd direct internal trade routes to it, or build more production worker improvements, or cash buy production buildings, or best of all, let it be a low production city that is instead good at doing what you placed it for, and just cash buy the key buildings it needs/
Thanks for the input. I think others have already addressed most of your points as to my thinking.
As Brandonito says, it is not a 50% bonus, it's a flat 8 hammers.
Sherbz pointed out the benefits of putting the IW in a coastal city. Since 9 times out of 10, my weakest production city is a coastal city, my thinking pretty much jibes with his.
And as neilkaz mentions, of course it's situational: If I'm going for an early victory (low difficulty level or non-deity domination or diplomacy) there's no reason not to put Ironworks in your capital or other best city. The other cities you have won't have time to take advantage of it. If you don't have a need for many national wonders (or built all you needed early before expanding), than you may not need it in a weak production city. And of course, there's always those occasional games where you have more cash than you know what to do with; in that case you can buy all those buildings the weak production city needs.
As a general rule of thumb though in a long game (science or very high difficulty), I find putting it in my weakest production city helps my whole empire more than putting it in an already powerhouse capital or Petra-type 2nd city...
As for trade routes, if I'm going for space victory, my trade routes all need to be for growth (for science) or cash (freedom 3rd tier policy buying parts). If I'm going for diplomatic victory, I need trade routes for cash or CS relations (ideology policies). If I'm going for cultural victory, I need trade routes with other civs for the tourism bonus. Internal hammer routes are always dead last on the trade route priority list basically. Food routes are best for any victory, and cash/diplomatic relations are often vital as well.
If I can spend 15-20 turns building an ironworks to mostly solve my slow building issues in a city, it's better than tying up a valuable trade route or spending cash I could use to buy a research lab, SS Booster, or CS ally. At least that's what I've found works better for me.