We've been to the south of France in June 3 times--perfect weather (dry and high 80s) and lavender season in Provence. You can easily drive to the Cote d'Azure to also get a beachy side to the trip. There's history and good food all around.Hawaii is also a good spot for June because it it right after their high season. We've gotten tickets 40% cheaper than in the winter to Honolulu in June.Also Argentina in June would be like their Autumn and a great time for vineyards and a decent daytime temp in the 70s but maybe not warm enough for beach/pool.Costa Rica, as someone else said, will be lower season, so cheaper and fewer tourists but there could be a lot of rain. We've been there and June and liked it. It only rained in the afternoon and it was very affordable because of the season.