What are the best day trips from Nagoya?

Inuyama over everything else for a single day. The keep was built in 1537 by Oda Nobuyasu, one of only 12 original castle towers still standing in Japan, and it's small enough that you'll spend 20 minutes inside rather than losing half a morning. The real draw is the town below. Honmachi-dori has about 400 meters of restored shopfronts selling dengaku (tofu grilled on wooden skewers with thick miso paste, ¥400-500 per stick) and local craft beer at Inuyama Brewing. One of you wants the castle. The other wants the shops. You'll finish the keep in under an hour, then meet on Honmachi-dori for lunch. North of the castle, the river hosts cormorant fishing boats (ukai) from June 1 through October 15 with evening departures around 17:45. Tickets run ¥2,600-3,600 per person depending on the boat. Charcoal smoke drifts across the water. The splash of cormorants diving in firelight. It's the best shared evening within half an hour of Nagoya. Take the Meitetsu express from Nagoya Station.

Ise Grand Shrine is 130 km south-east, 1 hour 20 minutes on the Kintetsu limited express from Nagoya Station (¥2,770 one way including the surcharge). The shrine complex splits into Geku (outer) and Naiku (inner), about 6 km apart with a bus running every 10-15 minutes. Start at Geku, which takes about 40 minutes to walk. Then bus to Naiku, the main event. The gravel paths through old-growth cryptomeria stay cool even when the temperature sits at 26°C with 72% humidity. Naiku needs about 90 minutes if you walk slowly. Okage Yokocho, the shopping street outside Naiku's entrance, is where you eat. Akafuku mochi, soft rice cake with sweet red bean paste, has been sold at the same shop since 1707 for ¥260 per 2 pieces. Tekonezushi (hand-pressed sushi with soy-marinated bonito) at the small restaurants runs ¥1,200-1,500. The whole trip works comfortably in 10 hours if you catch the 8:00 or 8:30 Kintetsu departure. Worth noting, the last limited express back leaves around 20:30.

Takayama is the trip everyone asks about, and it works if you're honest about the schedule. JR Wide View Hida from Nagoya Station costs ¥5,610 one way for a reserved seat, 2 hours 10 minutes through the Hida mountains. The 7:43 departure gets you in by 10:00. Sanmachi Suji, three parallel streets of Edo-period merchant houses, is walkable in 2 hours. The old wooden buildings smell like cedar and soy from the miso shops along Kamisannomachi. Hida beef is the draw. Vendors along the street press hida-gyu sushi onto rice crackers (¥800 for 2 pieces) that you eat standing at tiny counters. For a sit-down meal, Maruaki serves hida-gyu set lunches for ¥3,000-5,000, and the tatami seating feels right for a slow midday together. The last Wide View Hida back leaves at 17:38 (18:38 on some days), putting you in Nagoya by 20:00. That gives about 7 hours on the ground. The Takayama Festival Floats Exhibition Hall (¥1,000) finishes in 45 minutes if one of you wants a museum stop. Skip Shinhotaka Ropeway, 90 minutes further by bus.

For something low-key, Tokoname is 35 km south on the Meitetsu Tokoname Line (35 minutes, ¥630). It's a pottery town with kilns dating to the 12th century, and the Tokoname Pottery Footpath covers 1.6 km past brick chimneys and ceramic-lined walls. Several studios offer wheel-throwing sessions for ¥3,000-4,000 per person, about 90 minutes. That tends to be a stronger couples memory than another temple visit. Gifu, 30 km north-west on the JR Tokaido Line (20 minutes, ¥480), runs Nagara River cormorant fishing from May 11 through October 15. Observation boats depart around 18:45, and the masters handle leashed cormorants by torchlight. Tickets for the regular viewing boat cost ¥3,500-4,100. The fire reflects off the dark river water, and you can smell the pine-tar torches from 50 meters downstream. Mind you, the boats fill up on weekends. Book through the Gifu City tourism office at least a week ahead for Saturday dates. Meiji-mura, the open-air museum near Inuyama (founded 1965), has over 60 relocated Meiji-era buildings across a hillside. Combine it with the castle that same morning if you catch the 8:00 Meitetsu.