How to see the Loire Valley without a car (from the city of Tours)

I actually based myself in Blois not far from Tours and from Blois took a bus to visit Chambord (magnificent place to visit) and took the train same day to Amboise (Leonardo Da Vincini's house is their behind the castle) and Chenonceau (this the famous one bulit over the Cher river flowing under it) . The area is a magnet for tourists so the French have established bus and train transportation to get around without a car. You just have to do the research in the guide book to narrow down where you want to go. Then whatever you can't figure take a tour arranged by the hotels.
http://www.discoverfrance.com/european-tours-destinations/loire-valley-bike-tours?gclid=CjwKEAjwzKPGBRCS55Oe46q9hCkSJAAMvVuMmFz_My6Ttc6fs8Wu-CaRduxEotkUEDg2texgI_MWBhoC2J7w_wcB

Also if you are the adventurous type you can rent a bike and tour the Chateaux.
http://www.cycling-loire.com/

It's a 20 minute train trip from Tours to Amboise. The Chateau d'Amboise is charming, and the Chateau Clos Luce (Leonardo da Vinci's house) is nearby. You can have a picnic on the grounds of either one or check out L'Epicerie for a reasonably priced, tasty lunch in a friendly place. We were in Amboise last week and enjoyed it very much.

A warning: Many places are closed in France on Sunday so it's best to check ahead to see if a restaurant that interests you or if the Carrefours (grocery) is open.

The Loire should be beautiful in May! Bon voyage.

As you only have 2 days in the Loire Valley, accept the fact that you'll only get a rather small taste of all it has to offer. Instead of trying to get from one destination to the next on public transport, it would probably be worth paying for a van tour.

Here is an example of a tour you could take from Tours. http://www.accodispo-tours.com/join-in-tours.html
and another https://www.tripadvisor.com/Attraction_Review-g661238-d2416128-Reviews-Loire_Valley_Day_Tours-Chaumont_sur_Loire_Loir_et_Cher_Centre_Val_de_Loire.html

I was in the Loire Valley last spring and didn't rent a car either. I easily saw all of the chateau I wanted to. I'm glad you'll be there over the weekend because on Sat, Sun, and Wed there is a chateau bus that leaves Blois at 9:33 and 11:33 and makes a loop to Chambord, Cheverny, Beauregard, and then back to Blois. You can see the schedule here. http://www.bloischambord.co.uk/organiser/pratique/transports/254973-navette-41-blois--chambord--cheverny--beauregard (you can click on the pdf for the timetable).

So, you'll just need to take the train from Tours to Blois, and then catch the bus right outside the Blois train station. Head out the front, walk straight, and slightly to your left is the bus lot. You can't miss it. Buy the 6 euro ticket from the bus driver and you can then ride the bus for the entire day. If you show your bus ticket at the chateau ticket window you'll also get a euro or two off admission. The bus ticket essentially pays for itself with these discounts. It's a great deal!!

To get to Chenonceau, one of my favorites, you can just take the train from Tours to Chenonceaux. It takes about 30 minutes and cost 7 euro each way. Check the train schedules for the return times. Once you get off at the Chenonceaux stop, you'll see a long gravel pathway that leads to the chateau. Along the way you'll see a maze and a small animal farm.

You will love the Loire Valley!! Have a great time.

You can ride bicycles. The valley is pretty flat, and there are nice routes.

Abby,

Dawn's detailed explanation is spot on:

So, you'll just need to take the train from Tours to Blois, and then catch the bus right outside the Blois train station. Head out the front, walk straight, and slightly to your left is the bus lot. You can't miss it. Buy the 6 euro ticket from the bus driver and you can then ride the bus for the entire day. If you show your bus ticket at the chateau ticket window you'll also get a euro or two off admission. The bus ticket essentially pays for itself with these discounts. It's a great deal!!

We stayed in Amboise and took the Navette 41 and visited Chambord and Cheverny chateaux.
We also took a public bus from Amboise to Chenonceau (our favorite) on a separate day.

Enjoy France!

I rode a bike in the area, but getting through Tours was the worst part of the trip. If I were staying in Tours, I'd probably go with van tours.

If you really want to use a bike, pick lodging close to the bike route. Depending on how well you ride, I'd guess two hours riding to get to Amboise (Chateau Amboise and Clos Luce). Up to a couple hours from Amboise to Chenoncaeu. Villandry is also a reasonable ride from Tours.