Do you speak Spanish? Have you traveled in Latin America before?

Public transportation in BA is quite comprehensive, but it's mostly bus-based. The subte (subway) system is relatively small and doesn't go directly to many of the places you're likely to want to go (for example, it goes to the very northernmost part of the Palermo neighborhood, leaving you to walk maybe 15-20 minutes to get to the heart of the Palermo Soho or Hollywood areas; the subte doesn't go to La Boca at all, so you'll need to take a bus if you want to go there...) Also, the subte shuts down weirdly early at night, although buses run far later.

If you speak Spanish and are willing to ask locals how to get around, the buses are fine. They're not luxury by any means, but they're in decent condition and most of the routes run pretty frequently. You'll need to buy a SUBE card, which you can do at a machine in EZE as well as other locations, and you can add value at the machine where you buy it as well as in subte stations and in most "kioscos" (the little convenience store-type places you'll see all over the place); most of them will have a sticker showing the SUBE logo and either will have a machine to add value or will do it manually for you at the cash register.

That being said, there is all of one bus route that goes from EZE to the city - the #8. There are two varieties - an express and a local, which takes about two hours to Plaza de Mayo and takes you on a very long journey through some not-terribly-attractive working-class towns of Provincia de Buenos Aires. If I remember correctly, the local buses come every 20-30 minutes; I'm not sure about the express ones, as I've never taken them.

If you're flying in/out of AEP, by contrast, there are a bunch of buses that pass directly in front of the terminal building and will take you downtown in maybe 15 minutes, or to the ritzy parts of Palermo in about the same amount of time. AEP is a dream for transit.

If you're arriving at EZE and don't want to deal with the hassle of the bus, Miguel Tienda León has buses that take travelers directly to their hotels at a reasonable price point that will save you some cash on a taxi.

I believe Argentina removed entry restrictions for vaccinated travelers, but it's always best to check official sources for that information.

It's possible to be mostly cashless, but you'll get a much better rate if you convert USD to pesos at the unofficial, blue rate. There are explanations of how that system works here on FT, but from what I've read on other FT threads and also heard from a friend who went down last month, you can send dollars to yourself via Western Union and then withdraw that money in Argentina in pesos at something approximating the more advantageous rate. Another reason to have some cash is that you'll need it for public transportation (I don't recall the SUBE machines or the subte stations taking cards) and for anything you might buy from a street vendor, kiosco, etc. And I don't think too many taxis take cards - at least not in my experience.

I can't speak to what's up with Hyatt, but the last time I was there I stayed at the NH 9 de Julio. It was a very nice hotel, and I'd highly recommend it. I think I paid about $80-ish a night or something, but that was in 2019.