I would like this to be answered by a pilot who is a researcher.

Is there any aircraft frequency (or frequencies) legal for pilots in
two different aircraft, to talk to each other while in the air, and
not near any airport?
Perhaps the conversation would be about where to have lunch, or any
topic.
Is there a designated frequency for this type of personal
transmission?

Hi Clicker5,

The Federal Communications Commission has designated 122.750 MHz as
the frequency for "Private fixed wing aircraft air-to-air
communications."

Source:
47 CFR 87  (page 220)
Federal Communications Commission (FCC) regulations
http://www.fcc.gov/Bureaus/Engineering_Technology/Documents/cfr/1996/47cfr87.pdf
(PDF format, so the Adobe Acrobat Reader is required. If you don't  
have that, visit Adobe's web site:  
http://www.adobe.com/products/acrobat/readstep2.html )   

Additional sources:

"Freq is 122.750 for pilot talk and it is legal...."
Source: newsgroup message hosted by Google Groups 
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=393EB2BD.35BF267B%40jps.net

"122.75 is the preferred air-to-air frequency."
Source: newsgroup message hosted by Google Groups 
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&client=googlet&selm=tE5N8.1%24hk1.23605%40news

"122.75 is an air-to-air frequency, mostly used for inane chatter
(better here than on 122.8 or .9)."
Source: newsgroup message hosted by Google Groups 
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&client=googlet&selm=3D2DA9D7.3575F58%40nowhere.org

"only 122.75 is approved for general use.  The other frequency,
122.85, is only available under certain circumstances that are
specified by the FCC.  If you use any frequency other than 122.75 for
air-to-air communications, you're probably violating an FCC
regulation."
Source: newsgroup message hosted by Google Groups 
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&client=googlet&selm=tnnlv3fralje54%40corp.supernews.com

"Air-to-Air is for communications between aircraft in flight. Although
used by many as a cell phone replacement, it really is for exchange of
flight information. For example, the AIM recommends that 'Pilots
operating in VFR corridors (in Class B) are urged to use frequency
122.750 MHz for the exchange of aircraft position information.'"
Source: newsgroup message hosted by Google Groups 
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=its5gs09uvsghecssv28mkd8i1r54lk6qa%404ax.com&prev=/groups%3Fq%3D122.750%2Bgroup:rec.aviation.piloting%26hl%3Den%26lr%3D%26ie%3DUTF-8%26selm%3Dits5gs09uvsghecssv28mkd8i1r54lk6qa%25404ax.com%26rnum%3D4

"...there is a frequency set aside for air-to-air chatter: 122.750."
Source: newsgroup message hosted by Google Groups 
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=cJ1y4.158%24A3.811%40saturn.ipass.net

search strategy:
google groups, rec.aviation.piloting, pilot, frequency, "air to air"

I hope this helps.

Thank you - good research
clicker5

Hello, Clicker.

Just adding a comment here to let you know that the "Add a Comment"
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Regards,
juggler