hi Carol, you'll get used to it gradually. I live downtown in Flatiron-Gramercy and when I first started riding, I rented a bike at a LBS near the park and walked my bike over to the park. I still don't like riding on the streets, but I do it.

Try:
--start off by just riding a block or two
--riding on the streets early weekend mornings
--get someone to ride with you (great confidence builder)
--try to take the same route each time (so you know the streets and the potential trouble spots)
--go out on group rides w cycling clubs--they often ride through the city to get out and that will help get your comfort level up
--riding on the streets to the bike paths

feel free to contact me via private message if you want more info re any of the above