hi!! I'm from Cordoba! I'm not living there atm, but i'm sure i can give you some tips!
first of all, i would suggest you stay in a hotel in the CBD. there are some well known hotels in the suburbs (such as the hilton, hiliday inn etc), usually next to shopping malls but you will have to take taxis to and from the CBD and it will make you r trip expensive. I would suggest you the Amerian Hotel, the NH panorama hotel, windsor hotel and tower. all of these have webpages so i'm sure you can find some reviews and prices online.
since you will be staying right at the heart of the city, you can just walk pretty much everywhere.
must see sites include the Plaza san martin where you will find the Cathedral and the Cabildo (old town hall). you can walk a couple of blocks up through a pedestrian street to see the Manzana Jesuitica, with some churches, the university, library, etc. then visit the theatre Teatro del Libertador and walk up to the Patio Olmos shopping centre to have lunch (just next to the theatre). After lunch you can walk a couple of blocks up the Av Hipolito Irigoyen and see the Buen Pastor Complex and the Capuchinos church. you will be now in the area called Nueva Cordoba, where all the students that come from all around the country live. you will find plenty of shops and bars here, but also lots of young people so maybe not the best place to stay cause it can be quite noisy at night. you can finish your day visiting the Palacio Ferreira Museum (also known as Eva Peron muesum). a couple of blocks up the same av. other must see include the Canada river ( runs paralel to the Av General paz, one or 2 blocks away from the theatre so maybe just pay a quick visit. if you are visiting on a weekend day, make sure you go to the Paseo de las Pulgas, a street market worth visiting in the evening) you can also go to tPArque Sarmiento, kind of a central park for Cordoba, you can visit the Ciudad Universitaria there, that's the campus of the public university and have some LOMITOS in a nice bar enjoying the outside. the Zoo is not worth going though, it not well mantained (or at least it wasnt when i left corodba).
to visit an estancia, the closest one to the city is in Alta gracia, maybe a 1 hour bus drive. you can find tickets at the bus station, and you can either go and come back in a day or stay there overnight to really enjoy the countryside. there are other nice estancias a little bit further away, around 90 minutes drive. they are all very pretty, my favourite one is Santa Catalina, around 90 mins away from the city. you can also stay there overnight.
make sure you try argentinian ASADO, and if it's in a local restaurant in the countryside it will taste better for sure. i hope you enjoy our wine too, and the gelattos are popular as well. one of my american friends fell in love with the bakeries hahaha i dont find them very special but the bread and cakes and biscuits are worth trying apparently!
well, i hope i helped you, i'm not a tourist guide nor a tourist so i'm sure i'm missing some information, so this is the government webpage for tourism, maybe you can get some more tips.
http://www.cordobaturismo.gov.ar/ (hope you can translate it with google haha)
oh i'm forgetting to tell you there is a double decker bus tour that leaves from the cathedral, if you dont feel like walking, and they explain all the history and stuff!
i'll be in Cordoba next year in march, so if there's anything i can do for you guys just let me know. I'd love to drive you around to the Estancias if I can fit it into my schedule hahaha I'm currently on a backpacking tour around asia, believe me i know how helpful a local can be... but well, not really sure what i will be doing by march 2014!