There are different types of sakura. Basically speaking, there are two. First, there are the "standard" type, which bloom first, typically in early April in many places. They have simple petals. Then there are "yae-zakura", which bloom later. They have complex (double) petals and are very bushy and full looking. The end of April or first part of May is pretty typical for yae-zakura here in Nagano Prefecture.
I'd skip Ina City, though. You're probably talking about Takato Castle, and they have the regular type at their big festival, which will be finished when you visit.
Nagano Prefecture in early May is a definite Yes! I'd say go to Matsumoto, see the major sights (the Japanese national treasure Matsumoto Castle, the Ukiyoe Museum, the Kusama Yayoi exhibition, Nawate Street, Nakamachi, and so on. Also, take the wooded trail from Joyama Park up to Alps Park in the morning, and look out over the snow covered Japan Alps lit by the morning sun. That's an awesome view! And you'll probably see some yae-zakura in town or along the trail.
Speaking of yae-zakura, some places in central Nagano Prefecture have special types, such as GREEN or YELLOW yae-zakura blossoms. (the variety names are gyoiko, ukon, and so on). Just search online for "green sakura blossoms" and you'll see what I mean. They are totally amazing to see up close. There's a university called Matsumoto Shika Daigaku in Shiojiri, Nagano Prefecture, that has a special yae-zakura festival usually at the beginning of May during Golden Week, so you might try to visit that. And there's even a free bus to the campus from Shiojiri train station.
If you get to that part of Nagano Prefecture, then also add Narai (also called Narai Juku) to your itinerary. It's cooler there, so any yae-zakura would probably be a week or so later. And the old buildings in Narai are awesome.
https://en.wikipedia.org/wiki/Narai-jukuGood luck!
