You wrote, “we’re trying to find a climate that is as similar to here as possible” but unfortunately, I don’t think there is an east coast beach climate even remotely similar to here. As someone who grew up in coastal Connecticut and vacationed up and down the east coast my entire life (and has now lived in SoCal near the beach for 7-8 yrs), I can tell you there is no comparison in terms of climate.
The biggest difference is the humidity. If you’re used to the dry CA air, you will suffer mightily in the east coast humidity. It can really zap your energy.
In addition, there just isn’t the same amount of sunshine. It’s very frustrating to plan a BBQ and have it be rained out, or to wait through a long winter of crappy weather only to be greeted with a rainy spring that then turns into a rainy summer. These things happen on the east coast, and frequently!
Granted, there are lots of other reasons to consider living on the east coast (many of which have already been debated here), and I’m a big fan of the east coast and miss it dearly, but for me, the climate here is the big swing factor. If you’re a lifelong Californian, I’d encourage you to think long and hard before making such a move if your hope is for a “similar climate” because it just doesn’t exist, and that’s difficult to fully realize until you’ve lived in both places and experienced it firsthand. At the very least, you’ll want to take an extended vacation there, especially in the summer months, to see how it feels. Best of luck!