Here's a sample:

Central Park SummerStage
When: May - August
Where: Rumsey Playfield, Central Park, 72nd Street & Fifth Avenue
What: SummerStage is one of New York's greatest summer institutions, filling Central Park with music, theater, opera and dance for two months each summer.

This is a very cool place to spend a hot summer night. The entertainment is top notch and the price for many of the groups is free or a $10 donation.

Directions:
Subway: to 72nd St
or to 68th St.

Metropolitan Opera _ Met In The Parks
When: June - August
Where: Selected parks in New York, New Jersey and Connecticut.
What: The Metropolitan Opera presents free opera at Met in the Parks, a three week mini-music fest.

Bryant Park Summer Events
When: June through September
Where: Bryant Park (40th - 42nd Streets, between 5th and 6th Avenues)

Make sure to check out the Bryant Park Summer Film Festival which screens classic films at Sunset on Monday nights, and the other free concerts and events live at Bryant Park:
http://www.bryantpark.org/calendar/jun.php

Directions: Bryant Park is situated behind the New York Public Library in midtown Manhattan, between 40th and 42nd Streets & Fifth and Sixth Avenues.
Subway: train to 42nd Street/Bryant Park
or to 5th Ave.

NYC River to River Festival
When: May, - September
Where: Lower Manhattan
What: Just about any event that could interest you. Food, music, dance, drama, walking tours, 4th of July fireworks, and more and more and more...

Starting at the end of May, the festival goes through the summer until the end of September. Restaurants feature seafood extravaganzas and wine tasting, midday and evening events are planned to cater to every taste.

You're guaranteed to find something you can't resist.

Hudson Riverflicks
When: July - August.Films start at sunset or around 8:30 PM
Where: Pier 54 West Street at West 13th St & Pier 25 West Street at N. Moore St.
What: Films shown down by the riverside and out beneath the stars in Manhattan. In one of the most romantic settings, Hudson Riverflicks entertains with cult classics and popular movies.

Enjoy all time great movies under the stars! Every Wednesday evening at Pier 54 and Friday evening on Pier 25.

Directions:
Pier 54: Take the A, C, E, to 14th Street OR take the M14 bus to Tenth Ave. and 15th Street. Cross West Street/9A at 14th and walk south.

New York Philharmonic
When: Beginning early July. Check the Web site for dates in July - Saturdays and Sundays).
Where: Central Park
What: The New York Philharmonic invites music lovers to pack a picnic basket and settle down on a blanket in the grass for free music in the moonlight at Concerts in the Parks.

Grucci fireworks, familiar to the world from the Macy's 4th of July displays, are traditionally a part of the show in most locations.

Mostly Mozart
When: Tickets go on sale in mid-May.
Where: Lincoln Center (64th between Columbus and Amsterdam)
What: Summer in New York means Mostly Mozart at Lincoln Center. It's the place where great classical artists, music devotees and casual listeners all join together to celebrate the music of Mozart-plus Beethoven, Schubert, Haydn, and other Classical and Baroque favorites. Well-known as a showcase for both world-famous performers and promising young artists, the Mostly Mozart Festival is especially popular for its informal, friendly atmosphere.

Directions:
Subway: Take the to 66th Street Station.

By Bus:The M5, M7, M10, M11, M66 and M104 bus lines all stop within one block of Lincoln Center

New York International Fringe Festival
When: August
Where: Lower East Side
What: This multilingual, 17 day, 180 production extravaganza includes only stuff you would see below 14th Street - in other words, off-off-Broadway. Enjoy almost two weeks of the weird, wild and wonderful as what is affectionately known as FringeNYC. This is the theater for those who are tired of glossy, corporate musicals and prefer the alternative, offering dance, puppetry, spoken word, multimedia and just about anything else you would care to name. The event is held every year on the Lower East Side of Manhattan, in 20 venues within 15 blocks of each other. All are easily accessible and surrounded by the streets and parks, in turn filled with free street entertainment, from fire-eaters to buskers, as well as a life-sized chess game.