The restaurant on the corner of 3rd Street is going to be called something like Stone House Cafe, I guess referring to the historic Old Stone House in the park nearby. I talked to one of the owners on Monday. He said he came from TriBeCa Grill, and his partner came from River Cafe. They are going to strive to have an interesting American menu ($15-20 entrees, if I remember correctly), but also to make it an accessible, "neighborhood" type of place (e.g., burgers too). Forgot to ask when they will open, but the construction looked almost done.
By contrast, the Joya II spot (bewteen 2nd and 3rd) still looks completely gutted. I saw, like, one fixture in there (a sink) and that's it! Not opening any time soon.