Question about chateaus in Loire Valley

Will you be staying in Amboise on your tour? For 2 days , it will take you at least 3 hours per chateau on the first day. First day do Chenonceau 3hrs, Château de Vaux le Vicomte 3hrs. Second day, do 4 hours for Chambord and a few hours in Clos Luce. Skip Villandry. For each Chateau, tour the most important royal rooms and the gardens. You don't have to see every room in the chateaux.

https://vaux-le-vicomte.com/

There is no train service to Vaux le Vicomte. From Amboise, take train to the Melun train station, than you'd have to take the shuttle bus which operates on weekends and holidays only or take a taxi:

We do not drive. So we have to rely on public transportation to get the chateaus and Ambiose.

You can take the train from Tours to Chenonceau and from Tours to Amboise.

Go to their web sites and get a feel for what interests you. We did Chateau Royal and Château du Clos Lucé in Amboise comfortably in a day. We spent a wonderful afternoon at Chenonceau. We went in May and the crowds weren't bad. August might be busier. If you want to stroll the grounds, budget more time.

Try to avoid "chateau burnout". It's like trying to do two or three museums in Paris in a day, you get overloaded. Even though we had an entire week in the region, we limited ourselves to just a few chateaux. There's a lot more to the region than castles.

I have no idea how you will get to all of these by public transportation, but it will certainly slow you down. I know Amboise and Chenenceau can be done by train. Likely a combination of train and bus to Chambord, which is furthest away to the east. Having a car is so much easier. Or getting an organized van tour. I would not plan for more than 2 chateaux per day on your own. Villandry is the more difficult to plan for, since it is the only one on your list that is west of Tours, but I think there's a bus. We spent 2-3 hours at each Chateau and Clos Luce.

You might want to check out a minivan tour, such as this site: https://www.accodispo-tours.com/

I'm using it to see 3-4 in one day since I'm not renting a car. I'm going to just see the highlights, i.e. concentrate on the gardens at Villandry vs. the chateau. Otherwise, it all starts to seem like the same general type of rooms.

Chateau de Vaux-Le-Vicomte is in a totally different area and has nothing to do with the Loire chateaus.

I am sure you can find a tour to get to the chateaus. As far as their locations (and possible groupings): Chambord is further away to the north; Chenonceau is relatively near Amboise; Clos Lucé is of course in Amboise, and Villandry is a bit to the south.

Villandry’s gardens are beautiful and well worth seeing. I have always purchased garden-only tickets there. You definitely can get chateau’d out!!

It’s a beautiful area.

Don't forget the Chateau d'Amboise right there in Amboise, looming over the city. You can walk up from the main street. I thought it was much more interesting than Clos Luce' (Da Vinci is buried on the Chateau grounds - not at Clos Luce'). And actually I found it more interesting on the inside than Chenonceau.

I would not plan on visiting more than 2 chateaus per day as you will be burnt out, plus relying on public transportation to get you around will really slow you down and limit what you can see
Plus there is so much more in the Loire valley than chateau, wineries, caves but for these you do need a car.