The Baan Tya Wang hotel (9 rooms) is located at the end of a quiet dead-end street along a canal connected to the Chao Phraya river. We got there after a 10 min drive from the train station. The hotel is run by an older couple that is extremely kind and helpful (although their English is average). It is designed by one of their sons in a beautiful mixed traditional and modern style. The entrance is a wooden construction that rests on concrete pillars, below which is made the reception, salon and eating place. The furniture is retro-design (or vintage?) with thai elements giving a very cosy atmosphere. On the first floor is a beautiful wooden room with lots of antiques. Behind this construction is a modern building that has the rooms. The rooms are beautifully decorated with Thai elements. Ground floor rooms have a terrace in front where you can comfortably lay down on a mat with a drink to enjoy the canal view. The garden is well designed with grass, small water ponds and sparse big trees, and literally ends in the canal (which is clean by the way, we saw big birds fishing there). Be aware that the water brings a lot of musquitos too, so bring DEET. Also note that there is a military camp across the canal, so you see and hear them training during the day (we didn't mind).
There is no swimming pool. Rooms have fridge, AC, flat-screen TV, and free tea and coffee. In the ground floor rooms, the shower is outside behind the room. There is free wifi everywhere. We got an extra bed next to the double bed that fitted our two kids.
The hotel serves European, English and Thai breakfast. We had the European one which was great: fresh fruit, yoghurt and toast. There is also a small Thai menu for lunch and dinner, which was good (if you like spiced food you should ask, the food we got was very mild).
The hotel has about ten bikes you can use freely to explore Ayutthaya. We used these to visit Wat Sri Sanphet and Wat Chai Watthanaram, but Ayutthaya is so small that almost any of the Wats worth visiting can be reached by bike. Two bikes had a seat behind which we used for our kids. They're adjustable in height. Traffic can be a bit hectic so avoid the bigger roads. If you prefer a tuk tuk, the hotel can book you one that brings you to several attractions and waits in between, a common way to visit the town (it's hard to catch a tuk tuk by yourself). Rate was 200 bath/h. The hotel also recommends good restaurants, and advertises boat trips for 1500-2500 bath.
The biggest pluses of this hotel were for us the calm and green surroundings, the beautiful decoration and homey atmosphere, and the unbelievable friendliness of the owners. If you're more into big resorts with swimming pools, cocktails, buffets etc, this is not the place for you.