Iridium is only a few block from Times Square, I think that's the nearest "name" club but taxis and trains make it easy to get around.
My suggestion is go online and check out some of the clubs' web sites....you can even get advance tickets online these days. I went to NYC for four days last fall and had advance tickets for shows all four nights before I left.
Here's a page where you can search for links to NYC clubs:
http://www.allaboutjazz.com/php/entity_search.php?t=7
Here's listings from the All About Jazz magazine for NYC for the 21st:
Thursday, July 21
Jazz in July: Portrait of Jim Hall with Jim Hall, Steve LaSpina,
Terry Clarke, Bill Charlap, Tom Harrell, Joe Lovano,
Peter Bernstein and others
92nd Street Y 8 pm $45
Jazzmobile: Lou Donaldson
Lyman Place and East 169th Street 7 pm
Steven Bernstein’s Millennial Territory Orchestra
Tonic 10 pm $12
Charles Gayle Trio with Hill Greene, Jay Rosen
Zebulon 10 pm
• Buddy Greco Iridium 8, 10 pm $27.50
Count Basie Orchestra Birdland 9, 11 pm $40
Pi Recordings Festival: Fieldwork: Vijay Iyer, Steve Lehman,
Tyshawn Sorey Jazz Standard 7:30, 9:30 pm $20
Mark Dresser; Catharine Jauniaux
The Stone 8, 10 pm $10
Jimmy Greene Quintet with Stefon Harris, Xavier Davis,
Vicente Archer, Eric Harland
Village Vanguard 9, 11 pm $30
Latin in Manhattan Festival:
The Music of Jobim, Getz and Tjader with Trio De Paz:
Romero Lubambo, Nilson Matta, Duduka da Fonseca with
Harry Allen, Joe Locke, Maucha Adnet
Dizzy’s Club 7:30, 9:30 pm $30
• Christos Rafalides and Manhattan Vibes with Mike Pope,
Steve Haas Dizzy’s Club 11:30 pm $10
• Edmar Casteneda Sweet Rhythm 8, 10 pm $15Thursday, July 21
• Deanna Witkowski Quartet with Donny McCaslin, Dave Ambrosio,
Vince Cherico The Kitano 8, 9:45 pm
Jeb Patton Trio Cleopatra’s Needle 8 pm
Tomas Fujiwara Group with Matana Roberts, Taylor Ho Bynum,
Thomson Kneeland Via Della Pace 9 pm
Ayana Lowe with Billy Lester, Bob Cunningham
Cornelia Street Café 6 pm $12
• Paulette McWilliams Smoke 9, 11 pm 12:30 am
• Bill Mobley Big Band; Mercedes Hall Quartet
West Bank Café 9 pm $15
• Tal Wilkenfeld 55Bar 6 pm
• Marta Gomez Jewish Museum 5 pm
• Arthur Sterling 5C Café 5 pm
• Robert Clemmings The Jazz Spot 7 pm
• Dan Stein Group Detour 9:30 pm
• Stein Brothers Quintet Kavehaz 9:30 pm
• Debbie Deane Band with Robin Macatangay, Stephan Crump,
Adrian Harpham Tea Lounge 9, 10:30 pm
• Ralph Lalama The Garage 9 pm
• Deanna Witkowski Bryant Park 3:30 pm
Mike LeDonne Quartet Citigroup Plaza 12:30 pm
The whole magazine is online here:
http://www.allaboutjazz.com/newyork/aaj_ny_200507.pdf