As stated, destination choice is an essential to happy travel.  Luckily, there are quite a few choices out there - a whole planet of them!  What follows are main suggestions only, not by any means a complete list, with several springboard assumptions:
-- Birders and non-birders traveling together
--First time visit
--Two weeks approximate duration. 
 
>PERU
Because it boasts the interesting extremes of Andes and Amazon, Peru is unparalleled.  Cuzco and Machu Picchu are the two main central mountain must-sees.  Manu and  Iquitos-area are the two areas of accessible Amazonia.  
>KENYA
It's perfect:  While the birder is trying to sort out the cisticolas in the nearby bush, the non-birder is oooing over the elephants beyond.  Plus an easy option:  Add in Tanzania and the Serengeti as well.
>AUSTRALIA
A great family destination, and very conducive to independent travel.   Queensland and the Great Barrier Reef area offer tropical birding and fantastic beaches.  New South Wales and Sydney area offer mountains and a complete Aussie experience.
>MEXICO
Despite it's proximity to the U.S., provides as exotic a destination as any.  Incredibly varied in habitats, culture, and weather (yes, areas even require a jacket!).  The Yucatan, Colima, and San Blas are well-known birding areas, and the former features the bonus of magnificent Mayan ruin complexes.   
>CARIBBEAN
Want to combine beaches and birds?  Lots of choices here.  Look into Jamaica, Puerto Rico, and Trinidad/Tobago.  The Caymans and Dominican Republic also offer interesting birding, but most of the islands boast their own endemics.
>EUROPE
The birder won't get the huge species list that he/she would from some of the other mentioned areas, but if there's a history or food buff in your party, Europe certainly satisfies.  The British Isles contains unique birding:  Norwich, Wales, and the Scottish Highlands.  Another up-and-coming area is Eastern Europe.   
>GUATEMALA
A lovely country of volcanoes and lakes and jungled ruins.  The Mayan culture is very much alive and endlessly fascinating, and the birdlife is abundant in the varied ecosystems.  Make a loop in the central highlands and then take a flight to Tikal.
>ADDENDUM !
Other terrific choices await:  India, Taiwan, Thailand, Hawaii, Costa Rica, Galapagos/Ecuador, Uganda, Brazil...