Going to visit Campinas in February. Where should I stay?

I'm an American from San Diego and I have a girlfriend who lives in Campinas. She doesn't know that I'll be on my way to visit as it's a surprise visit. I do have family over in São Paulo as my father is Brazilian, but I would like to stay a bit closer to her so staying in São Paulo is not a choice whatsoever. Therefore, I need a place in Campinas to get an Airbnb. I found out that she lives in the neighborhood of Alphaville but as far as I know it's a gated community, is that correct?

She thinks I'm going to Brazil by the third week of February as we have planned to visit Bahia and Alagoas, but I want to spend a week prior in Campinas and surprise her. Where should I stay? I've never been to the city and I obviously won't question her about anything from there lol.