Which of the following is not permitted in an R-2 zoning district?

In an R-2 zoning district, which primarily accommodates residential uses, the primary focus is on housing and related activities. A boarding house is typically characterized as a commercial use where multiple individuals rent rooms, usually for longer stays, and may share common facilities. This type of operation can introduce a form of transient occupancy and potentially impact the residential character and density expectations of the R-2 zone.

In contrast, the other options align more closely with the intended uses of an R-2 zoning district. A public parking lot may support residential uses without detracting from the residential nature of the area. A two-family dwelling fits directly within the residential use category, as it allows for multiple family units on a single lot. Additionally, a recreation center can be designed to serve the community within a residential area, promoting healthy living and social gatherings, which are generally considered compatible with the residential character of R-2 zones.

Thus, the boarding house is not permitted in an R-2 zoning district because its use as a commercial entity does not adhere to the residential intent that defines this zoning classification.