somehw I missed this topic, sorry for the late reaction.
It would be easiest and cheapest to climb Cerro Plata. It is nearly 6000m, non-technical and close to mendoza.
Even if you only hike up to BaseCamp or a bit above, you could spend a few days above 4300m. If you bring full cold weather gear, then you could try for the summit or at least for the col at about 5000m, from which you can see Aconcagua as well (see this picture her: http://exposedplanet.com/aconcagua-from-cerro-plata/
taken from the summit of Plata).
There are no park fees, so you can go really cheap. I would recommend to rent a porter or amule if you are staying longer than a few days (you need 5-6 days from/to Mendoza to summit). If you want an organised trip, that is possible, but expensive as it needs to be a private trip.