01/05/2011 AT 6:15 PM ET
Meg Ryan and John Mellencamp are no longer keeping their romance under wraps.
The new couple, who a source says began dating about seven weeks ago, were spotted together Wednesday in New York City,
They dined at E.A.T. before taking in an exhibit together at the Whitney Museum. On Tuesday they were seen grocery shopping at the Gourmet Garage in SoHo.
Last month the rocker announced his separation from wife Elaine after 18 years of marriage.
Reporting by MARY PARK