Stand pretty much anywhere in Nagoya with an elevated view and look northeast. You’ll see a small mountain range slowly being eaten away by a quarry. If you keep your eye on that mountain range but move left ever so slightly you should be able to make out the three peaks of Mt. Miroku (弥勒山), Mt. Ōtani (大谷山), and Mt. Dōju (道樹山).
Those three peaks bordering Kasugai and Tajimi (and therefore Aichi and Gifu prefectures) are some of the most accessible and enjoyable half day hikes in the greater Nagoya area, and along with Hasso in Inuyama (also bordering Gifu prefecture), have become my go to hikes as they are all so close to home. Take a look on Yamap and you’ll see that there are plenty of trails, plenty of access points, and plenty of places to park a car at the bottom. But don’t drive, ride your bike there (you can lock it up at the botanical gardens) with some trail running shoes or hiking boots strapped to you bike or in your backpack and get the best of both worlds. It gets busy at weekends so aim for weekdays or evenings (take a headlight) whenever possible, or even better miserably wet days which are my favourite. But even then you are unlikely to be the only one out there.