Hi again, Prachi! I am from Westchester - my dad still lives in the northern part of New Rochelle, on the Scarsdale border. I have planted a small rock garden at my parents' house for years. Every year for Mother's Day!
That said... some of the best plants I've had success in the shade there are impatiens. They are annuals, but spread very nicely and come in many colors. If you like leaves with color for shade, there are many varieties of coleus. They do get a flower
spike but it is insignificant and takes away from the pretty leaves.
For sun, I like dwarf zinnias - I've been growing
these from seeds
the past few years and they spread and fill a small garden nicely. They come in pink, white, or orange. There are also new guinea impatiens that can take the sun now. The flowers
are larger than the shady impatiens, and there are different colors for each.
Then there are flowers
from bulbs. Daffodils, crocuses, and hyacinths are the first to bloom in early spring
. Then you can grow lilies, gladiolas, and all sorts of other bulbs.
You haven't said if you want to plant each year, or have perennials. The thing about perennials is that they usually bloom for a shorter time than annuals do.