It's worthwhile getting the yellow fever vaccine, as travel restrictions can be imposed suddenly in the case of an outbreak. It would mostly affect travel to Paraguay, the northern Argentinian provinces, and possibly also Brazil.
Mosquito-borne diseases are becoming a major problem in Buenos Aires. Dengue is pretty much endemic, there's a two-dose vaccine for it. Chikungunya and Zika have been seen, I believe. So far this summer has not been too wet, so we've been spared the worst.
There are good vaccine clinics in and around Buenos Aires, like Vacunar and Centralab.
Argentina developed its own Covid vaccine (protein-based, non-mRNA) which is available in the clinics. Also available is the two-shot Zovirax vaccine, if you want to avoid shingles (nasty, two family members have had it).
Just to add, in CABA, according to a recent announcement, you will not be able to use the public health system without a DNI. I think province (PBA) is less restrictive. The clinics mentioned so far in this thread, are, of course, private.