Unfortunately, there's no good way to get to or near Edgewater from Connecticut on mass transit. Edgewater isn't served by any train lines. Neither Amtrak nor Metro-North will get you very close.

That being said, if you really want to take transit as far as possible, you can pick up Metro-North at any stop on the New Haven Line. Many stations have free parking on the weekend. Which station is the best for you depends on where you are coming from. If you are near New Haven, West Haven and Milford both have free weekend parking. If you want to go during the week, parking will generally cost $5-$10.

Here are some options:

1. Metro-North and Uber: Metro-North to Harlem-125 St. Take an Uber to the spa. This Uber ride will be at least $50 each way. Note that the ride could easily be over $100 if there is traffic or surge pricing.
2. Metro-North and Bus: Metro-North to Grand Central, walk 15 minutes or take the Times Square shuttle train to the Port Authority. At Port Authority take a bus to Edgewater.
3. Metro-North and Ferry (Weekdays only): Metro-North to Grand Central, walk or take a cab to the 39 St Ferry Terminal. Take an Uber or walk a mile to SoJo.