Serviceberry or Amur maple? For us those are around that size.

I'd plant something that would provide value in the summer, when you will using the proposed outdoor space more often.

A Sweetbay Magnolia (Magnolia virginiana) would be quite at home on Long Island. Lemon scented flowers in June, evergreen or deciduous selections, multistem or single trunk - I think you could be very happy with that plant.

Amelanchier, malus,sorbus and crataegus are generally good all year round plants - blossom, new foliage, fruits or berries, autumn colour and graceful winter architecture. Many choices to suit all sizes and aspects.

How wide is the gate opening? What is the measurement from the back of the circle (the part closest to the gate) to the gate?

Do you have enough room to open the gates fully and allow people (and perhaps machinery?) to pass if you put both a pergola/swing and a tree with a 10-15’ spread behind the circle?