hey joyc,
where to spend their vacation, depends on your parents' interests and habits.
barcelona is a great city, of course, and as they will be flying into there, a stay there makes sense. however i would recommend to spend more centrally, e.g. in madrid. madrid is packed with attractions and museums, has an excellent subway network and english is - more or less - spoken or at least understood. Madrid info: http://www.esmadrid.com/en/portal.do
as you are saying "the warmer the better", a stay in the nations's south could make sense. one of my favorite cities in spain is cordoba. with 320,000 inhabitants it is medium-sized and not too expensive, the climate in may is warm to hot. and in may the city is full of events, including the famous patio festival. these links (in english) might be helpful: http://www.cordoba24.info/english/html/events.html, http://english.turismodecordoba.org/index2.cfm?codigo=0540
other pluses of cordoba are its central location with highspeed train connections to madrid (less than 2hrs), seville (45 mins), malaga (1hr), the moderate size (major attractions such as the legendary great mosque can be reached by walking), and less expensive accommodation compared to larger cities.
granada is another famous city in southern spain, widely known for its remarkable alhambra fortress.
the southern coast may be hot in may, but may be pretty cool due to a fresh breeze from the sea. malaga has several good museums, but that is it (my opinion). ronda is a picturesque town your parents should not mis if they opt for the state of andalusia.
though it's gonna be a once-in-a-lifetime vacation, your parents will have to come back for more.... anyway, good luck with vacation planning.