Reader: We will be visiting NH in mid-May. We have a day and a night completely free and would like to experience NH at it's fullest. We will be flying into Manchester and Mt. Washington is our final destination.
What is "castle in the sky"? What do you suggest, please?
Lisa: The "Castle in the Clouds" (http://www.newhampshire.com/nh-attractions/castle.aspx) is actually a resort/estate that offers 45 miles of hiking trails. The views at the top are really beautiful. I don't know what you like to do so I'll have to give you some general information. If you like to hike and be in a natural outdoor setting, I would definitely recommend the Flume (http://www.newhampshire.com/nh-attractions/flume-gorge.aspx). That's one of the best natural attractions in our state.
We also have a list of 10 Things to Do in the White Mountains: http://newhampshire.com/explore-nh/10-things-white-mountain.aspx
And, 10 Things to Do in the Lakes Region: http://newhampshire.com/explore-nh/10-things-lakes-region.aspx
Depending on whether you'll have children with you, there are other activities that I would recommend. I do think Lake Winnipesaukee is one of the most scenic places in the state, outside of the White Mountains (where you will already be heading anyway). So, if I had to recommend something outside of the White Moutnains, it would be a trip to Lake Winnipesaukee. You can take a train ride around the lake (http://newhampshire.com/nh-attractions/winni-railroad.aspx), a boat ride across the lake (http://newhampshire.com/nh-attractions/mt-washington-cruises.aspx) or some shopping at the Tilton Outlet Stores, http://www.tangeroutlet.com/tilton. Wolfeboro is also a great little town on the edge of the lake.
You could do a tour of covered bridges. There are many located throughout the Lakes & White Moutain Regions: http://newhampshire.com/covered-bridges/bridges-listed-by-town.aspx.
If you have specific interests, it might be easier to point you in the right direction. If you like hiking, I can recommend some good hiking trails. But I would need to know if you'll have children with you, as some of the hikes lead to sharp drop offs and I wouldn't recommend them for kids. Also, if you have kids, you might want to try a place like Gunstock or Attitash's Alpine Slide.
Here is another page that will give you some ideas: http://newhampshire.com/explore-nh/nh-101.aspx
Most important, enjoy your stay in New Hampshire! Let me know if I can be of further assistance.