is costa still in your plans?
in june, it pretty much rains in the whole country, so levels should be up (not peak, though). also, it won't be dumping on you all day, you can count on sunny mornings to do what you like. no whitewater near the pacific NW, you'd have to move further into the country (sarapiqui or turrialba) or at least down further south. if you want to stay near the beach, the town of quepos (middle pacific) would be a good bet, with good easy/intermediate boating nearby, on the naranjo and savegre rivers. you'd also have the general river within a few hours' driving time.
there's also decent boat rental options, so you don't have to haul yours down (maybe bring skirt, pfd and helmet, and a short top). i'm a local costa rican boater, and i can help set you up here, just PM me for contact info.