Are there any Catholic schools in the town of Poughkeepsie?

Yes, several. First, two schools I attended that happen to be close to one another: St. Martin de Porres (PK-8) and Our Lady of Lourdes High School. If you want to get technical, St. Mary's Elementary in Wappingers Falls lies within the Town of Poughkeepsie.

I'm not sure if Holy Trinity (another elementary) is in the Town or City of Poughkeepsie because it's right on the border, but it's probably in the city now that I think about it. All of these schools are highly regarded.