I want to explore the castle town and take a dip in the hot springs! Can you recommend a place to stay near Inuyama Castle?

I want to go to the castle town of Inuyama Castle in Inuyama City, Aichi Prefecture, which is a hot topic right now, take photos of cute sweets that look great instagrammable, and eat them! Are there any recommendations for accommodations within walking distance of Inuyama Castle?

After sightseeing at Inuyama Castle, I would like to stay at a nearby hot spring inn.

I'm going to Inuyama Castle because I enjoy visiting castles. I'd like to stay in the surrounding area, so please introduce me to some hot spring inns. If they have an open-air bath, that would be great.