Connecticut pizza gives NYC a run for its money! Take time to go to New Haven (travel time dependent on traffic) and check out iconic pizza joints; Pepe's, Sallys, Modern, & BAR.
New York City is nearby and accessible via train (1 hr). Spend time shopping, eating, seeing a Broadway show or just walking around and explore what the city has to offer. To get to NYC from Stamford: The Metro North train will take you direct from Stamford Train Station to Grand Central. From there, you can go anywhere in NYC via subway (if you are feeling brave) or cab/Uber/Lyft