Hampton Bays
From your new location, you are sitting on some of the best fly fishing spots on the island, even shore-bound. You've got the entire back sides of Shinne**** and Moriches to explore.
If I were you, I wouldnt even bother with the Peconics. Unless you were gonna try for some spring tide runner weaks.
Get out there as the spring starts to melt away the winter blues. Note how the tide drops and exposes bars, mussel beds. Check out the creek mouths. Enter all this into a log so that you can get a fix on how much you'll need to subtract from you shore tide tables. Maybe even take some casts in the day so that you can get used to how it feels in the currents.
The start going fishing for real around mid-late April. Stick with dusk and nights, esp when the tide is falling into dusk/dark. Keept at it and you'll have a nice bass on the fly by the 1st week of May!