From Gossip Cop:
The updates have become so frequent, Gossip Cop decided to simplify the listing of confirmed Eclipse cast TV appearances.
A running list is below, with additions to follow…
***** ***** ***** ***** ***** *****
June 14 – Robert Pattinson – “The Today Show”
June 15 – Robert Pattinson – “The Tonight Show with Jay Leno”
June 28 – Taylor Lautner – “The Today Show” and “Live with Regis and Kelly”
June 28 – Kristen Stewart – “The Late Show with David Letterman”
June 29 – Kristen Stewart – “The Today Show” and “Live with Regis and Kelly”
June 30 – Kristen Stewart – “Lopez Tonight”
July 1 – Taylor Lautner – “The Late Show with David Letterman”
July 6 – Nikki Reed – “Live with Regis and Kelly”
July 7 – Bryce Dallas Howard – “Live with Regis and Kelly”
Thinking of Rob 
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What day is the Jimmy Kimmel show airing?
I believe the Jimmy Kimmel show is airing June 23