The aptly named Loews Miami Beach Hotel is probably perfect for your needs. It's very popular, and few have had anything negative to say about it. If that's outside of your price range, though, there's always the Sense South Beach Hotel. It's hard to get much closer to the water than that!
Flamingo Park is praised as both a lovely place to visit and a pet-friendly playground perfect for the whole family, including the four-legged variety. You'll find it on 11th street, but in case it's not the perfect place for you, keep South Pointe park in mind as a suitable alternative.