Will have a 36 hour (2 nights) layover in GRU. Looking for a hotel close to Guarulhos, preferably with local restaurants and/or bars around it. Also, whats the nearest good churrascaria/rodizo, and how much should a taxi run?

Guarulhos is an actual town, so has the amenities of a small town including restaurants, bars, etc. I've just passed through, so can't give specifics. Someof the hotels have free airport shuttles.
But with a 36 hour layover, I'd go into Sao Paulo city itself (about an hour)and stay there (unless you really just want to sit by a pool out in Guarulhos). Much more to do and see .....and eat. Try Jardins or Vila Madalena neighborhoods. There's a shuttle bus (about R$35).

I second the advice of heading into S�o Paulo itself - Guarulhos itself is the epithome of an ugly/uninteresting town. Just make sure factor in the time/cost since it can take upwards of 2hrs to get to/from GRU during rush hour.

In S�o Paulo, you will also find better, cheaper accommodation. Lately I've been picking Accor hotels (Mercure) which have plenty of options, somtemies well under U$50 per night.

For churrascarias, you will want Fogo de Chao (Morumbi) or Barbacoa (Itaim branch, on Renato Paes de Barros Street) for rodizio. If a la carte, I highly recommend Figueira Rubayat in Jardins, for a unique setting under a sprawling fig tree.

If in S�o Paulo, don't forget to try the sushi: it's the best outside of Japan. Nagayama, Shigueru, and Koyama are some of my favourites.