We stayed in Amboise last summer and it was lovely. Booking.com had an amazing deal on a vrbo type carriage house next to downtown center (there were 5 of us so we needed the space). We walked out every night for dinner, had a garden for glasses of wine, etc. Lots of lovely accommodations in Amboise.
Amboise was conveniently located for many places in each direction. Lots of chateaux, but don't overlook the amazing ZooParc de Beauval! My adult daughter and I went, and it was as good or better than the San Diego Zoo, very easy to get to, etc. About an hour drive from Amboise and IMO totally worth it to give us a break from days of awesome chateaux and history. But it was so much walking. The giant pandas were right there and so amazing, we loved the three story viewing pavilion over the hippos -- you could see them from waterlevel and from above, which was neat. So many birds - if you are a bird-lover, this is your place. Arguably the best zoo in Europe.
Agree that there is not much in Chambord other than the castle. We were driving from Paris, stopped there on the way to the Loire, enjoyed the roofs, and moved on. I would not want to stay in the inn on the grounds of Chambord itself b/c the crowds (in August) were crazy, the waits for anywhere to eat other than a quick coffee were very long, and it's very isolated.
Chenonceaux was lovely, but likewise, out in the country. My in-laws spoke very highly of Azay-le-Rideau b/c they really like historic fabric (didn't see it myself, we came in from different directions and met in Amboise). I think basing in Amboise itself, especially for a solo traveller, great.
FYI, it's really a one chateau a day thing - there is a ton of walking at all of them, and we're in good shape, but one chateau takes it out of you and the rest of what we wanted to do each day was just poke around markets and hang out with a glass of wine and relax in a garden with coffee. I sketched a little bit at Chambord when I needed to rest.