Hello, finally found time to come back.
Regarding flights: Norwegian have been documented as being in financial peril for ages now, so who knows what the truth is. Obviously it's up to you, but we used them several times in 2018/early 2019 (we were living in BA) and as I said, the Premium Economy was only marginally more expensive than BA Economy (if at all) and significantly more comfortable.
We flew from BA to Salta in Sept, and BA to Ushuaia around the same time. I think the flights were quite expensive £150-300pp - but I was quite fussy about flight times as we were going with a baby and I wanted to make life easier. Latam btw are appalling. Travel with them only if you HAVE to, and expect delays. Hate that airline. Aerolineas Argentinas are fine.
In BA, if you don't speak Spanish, stay in Recoleta or in Palermo Soho as people have mentioned. Puerto Madero is the financial district, all high rises and modern buildings, and poorly connected. Other parts of the city are actually quite dangerous, so do be careful. (Read up on the usual scams, esp with taxi drivers who are practically a mafia. I used Uber a lot, despite it not being legal at the time, because the drivers were more honest - I never had an issue, unlike in a taxi. Taxis do things like accelerating the meter, claiming prices are in dollars not pesos etc.)
The Evita museum is very good and amusing propaganda. The Museo de Bellas Artes has impressive exhibits and a permanent collection of Rodin, as well as modern art. MALBA and MAMBA are good galleries if you want modern art, and there's a beautiful collection from a private philanthropist in Puerto Madero - I've forgotten her name unfortunately. The Xul Solar museum is a bit trippy and a great example of Argentine work from the last century. I highly recommend the hop on, hop off buses; buy the 24h ticket around 3pm and then you can do 1/3 routes at 3pm before dinner, and the other two the next morning before your ticket runs out. It's a big city, so save your poor feet!
With food in BA, you've got to go to Don Julio's steak house. You're not vegetarian, are you? The beef in Arg is to die for, but there are a number of vegetarian and vegan places popping up, if so; BA is pretty "cool" and trendy.
AirBnB would give you some great places to stay, I'm sure! We never used them, but I happily would in your position. It's not a cheap place to visit, but the metro and bus are extremely good value and eating out is very acceptable too.