Normally May and June are warm (upper 80's), breezy (10 mph), lots of blue sky, but prone to some rain/thunder storms. The rain is warm and shouldn't stop you from enjoying your excursions.
I've never stayed at Capt Morgan's but it does look just like the brochures! It should be suitable for you and your friends. Close to town for dining and shopping convenience, but far enough away to avoid the hustle and bustle.
Have a great visit.