I truly don't recall the prices, but have made your exact trips several times, most recently last year.

When you arrive at AEP, there's a taxi line and depending on the flow, there could be quite a line of people or you could just walk up to the front. However, it's relatively organized and I've never found it to be an issue. At one point they had a system where you could scan a QR code that then allowed you to enter your destination and a pre-determined fare would be printed on a receipt that you then handed/showed to the driver so they couldn't charge more. However, I truly can't recall that I did that last year. It's not far to the Park Hyatt and shouldn't be too much. You'll need cash - even though the taxi may say it accepts credit cards, I've never actually tried that in Argentina. It seems this will your last leg in Argentina, so hopefully you'll already have some ARS. In all my trips through AEP, I've only once tried to use an Uber and it was a bit of a pain to find the pick up area and coordinate, so I've always been perfectly happy to just use a taxi. They're usually the typical black and yellow radio taxis and it's a fairly straightforward trip to the Hyatt, so they're not going to veer much out of the way to try and charge you more. It's not expensive and I've just not found this trip worth the effort of a booked car. The only taxis that I think are sketchy (just being judgy on my part) are the guys who try to pick up at the median/island where they're not supposed to stop because they don't want to get into the taxi line if it's busy/crowded.

When you head to the Hyatt, make sure you know if you've booked a room on Palace side or Park side as it's a bit of a pain to walk through the underground tunnel if you've arrived on the wrong side. Alvear for the Palace, Posadas for the Park, just give your driver the correct street.

As for Iguazu, it's been a few years since I made the Brazil-Argentina crossing, but I don't recall it being too expensive ($50USD or less?) although it's a bit of a drive and the driver has to stop and help you with the border crossing formalities. If you're coming from the hotel, I'm sure they can call you a taxi and assist with ensuring the pricing is reasonable. The Melia to IGR is actually closer than if you were heading from Puerto Iguazu so not far. However, i think I've always just asked the hotel to call a taxi for me.

When heading from the Hyatt to EZE, you can have the doorman hail a taxi for you or you can pre-book with Tienda Leon or Taxi Ezeiza, it all comes out around the same (about $40USD - at least that's always the figure I have in my head). I'm not sure why, but I generally just take a taxi to EZE but use a service from EZE into town. I can't recall why I do this, but it's been a habit/routine that's just developed over the past 15 years and it's worked for me. If you prefer a prebooked car, it's pretty simple to reserve online.

Overall, I've not found taxi drivers to be the scam artists they are made out to be on the forums and certainly not like in other cities. Years ago, they used to warn about $100ARS bill switcheroo but that seems a worthless endeavor now with the money being worth very little. I've only once had a driver that drove a bit out of the way to drive up the fare, but even that was a small amount. I've also had very nice drivers and one time, had a driver who was hopefully lost and he felt so bad he turned off his meter and said he wouldn't charge me.