Stamford is a real hot area for many species. You won't even have to travel all the way to Execution Light to enjoy it. As far as the striper run you read about, the bulk of the larger fish move through the area from Late April to the end of June with the peak being around the first or second week in June. After that, many of the larger fish either move very deep or don't return until the Fall.
My best advice is two-fold;
For starters, visit your local tackle shop and pick the owner's brain. Bring some cash with the intentions of purchasing the bait, tackle, etc... that he/she suggests (cash paying customers always get good advice). Ask as many questions as you can about location, technique, etc...
Second, purchase "Captain Seagull" fishing charts. Because of the location of Stamford, you might want to purchase both the Western Sound and the Long Island Sound charts. The first is a close-up, detailed chart that only covers the Western terrain. The second has less detail but includes the entire sound all the way to Orient Point.
Getting back to your original question, in the Spring and the late Fall, the entire area around the Execution Light is productive for Stripers. The key is to locate the bait, then anchor in the general area if you are fishing with chunks or clam bellies. The currents can be a bit insane in that area during the moon tides, but so can the fishing.