Visit other chateaus nearby
I'm not sure this qualifies as "off the beaten path" since these are also famous chateaus. However, Amboise is a good base for exploring the area since it's easy to drive and to get in and out of town. There are many wonderful chateaus within an easy drive so take advantage of it and visit:
Chaumont, east of Amboise on the Loire, is a gorgeous chateau with magnificent river views and magical gardens. Check Chaumont on VT to see photos of the gardens. There is a garden competition every year with a different theme and it is fun to visit: My VT Chaumont garden site is at http://members.virtualtourist.com/m/tp/1c57b6/
A bit further up the Loire river is Blois, a busy city with a magnificent chateau. Here's a link to my Blois site on VT. http://members.virtualtourist.com/m/7ba16/20e19/ and I encourage you to type Blois into the VT Search Window and check as many pages as you can. There are some wonderful Tips and Reviews on VT and it's lots of fun to read them and look at the photos.
Continue on to Chambord, not on the river but the largest Loire chateau and very impressive. There is also a very nice equestrian show at Chambord. There are other activities too and it's a great place to take children. http://members.virtualtourist.com/m/7ba16/1ff30/
Moving inland there is Cheverny, a beautifully furnished chateau, and you can watch the feeding of the hounds. The grounds are lovely too and there is a wonderful vegetable garden. http://members.virtualtourist.com/m/7ba16/1f8cc/
We enjoyed the medieval chateau at Fougeres-sur-Bievre. It is set up as an educational chateau so there are exhibits both inside and out. It is a very impressive building in a tiny, very neat little village. There are animals in the garden the kids (or you) might enjoy. http://members.virtualtourist.com/m/7ba16/1e12e/
Headed south but still near Amboise is Montrichard with a small chateau and a wonderful raptor show. If you enjoy birds and falconing, this is a must-see. http://members.virtualtourist.com/m/7ba16/18d8d/
Back in the direction of Amboise, visit Chenonceau on the river Cher. This is the magical white chateau that is built across the river. It is nicely furnished and has two magnificent gardens. There is also a small farm area where you can view (and pet) animals and walk through the potager garden. http://members.virtualtourist.com/m/7ba16/1f949/
And you are now nearly back to Amboise for a lovely dinner in town and a walk along the Loire before bedtime.
On another day you can head west and visit Tours, Villandry, Luynes, Langeais, Usse, Chinon and Azay-le-Rideau, my personal favorite chateau.
Go to http://members.virtualtourist.com/m/7ba16/28/ and scroll down to the Travelogues. I have photos of 16 different Loire Valley chateaus. These are all famous ones but be aware that you can visit nearly any town in France and find a chateau, often open to visits. They vary from medieval to classic and are in varying states of repair but all are interesting and most have wonderful views from the towers. This was to keep an eye out for the enemy in times gone by but it gives tourists today great views!