If flying into VCP I assume you are flying Azul as it is the dominant player at that airport.
Personally if you are planning on spending the next day in Sao Paulo and arrive in VCP in time for the last departure of Azul's free bus transfer to Sao Paulo(leaves at 23.15), I would go into Sao Paulo on arrival, stay the night there and then you could leave your luggage at your hotel while you wander the city the next day.
A hotel like
http://www.laguardia.com.br/ is less than $US100 (cheaper through other webistes) and this one has the Airport bus to GRU (from where your KLM flight departs) stop right at its front door.
I've stayed in Campinas but never by VCP airport so can't offer any other advice.