June is usually dryer, sunnier, and cooler (good for sightseeing) in Rio. It's OK to sit out on the beach on a sunny afternoon, but too cool for a New Englander (i.e. used to cold water) to go in the water.

March can be rainy in Rio, and lately it has been. It also can be quite humid in Rio. There is even a well-known song about the rain in March.
Semana Santa (Easter week) is a week when a lot of people travel, so popular places are booked up way ahead.

Other parts of the country are in distinctly different climate zones, so you can usually find someplace that has good beach weather if you are prepared to fly domestically.