We went to Minneriya, which was a great day. A bit of waiting around but it wasn't too bad. We were there in August so we saw quite a few. You'll be in the blazing sun so definitely take hats and top up on sun cream. Anywhere else catch your eye? The food is amazing!
Have a look at the Selective Asia website: they have really handy maps showing weather each month and good places to go. We've used them twice to book Far East trios and they are great (and good value).
Whatever you do, try to climb Sigirya. I am old and was prompted to do so by my love of Duran Duran videos in the 80's. 😮 So worth it. Fine with small children with a bit of extra help but a real experience. You feel like you're on top of the world. Sublime. Best hotel is the Habarana Lodge. Visit to Kandy is recommended too - we stayed in The Citadel which was traditional and not too flashy. We loved it and are sure you would too.
Think about Kerala India - elephants, back water boat ride with your own chef cooking for you and your family, beautiful temples. Not sure about the beach.. grew up SE coast of India so never done a beach resort type holiday there. Wherever you go you will have a good time.