The fastest way to reach Kouzushima is by a 45-minute flight from Chofu airport in Tokyo (not Haneda or Narita airport) via a small 19-seater propeller plane.
You can check the flight timetables and book tickets at the airline website - look out for the 調布 ～ 神津島 route. Do note that the baggage allowance is only 5kg per person and excess baggage is chargeable at 300 Yen per kg. You may request for your hotel in Tokyo to hold your bigger luggage until your return from Kouzushima or deposit your bigger luggage at one of the many left luggage facilities in Tokyo.

For the flights to and fro Kouzushima, although the seat will be assigned, I recommend for you to sit on the right side of the plane. As you land at Kouzushima, you will enjoy great views of the Tako beach and the white cliffs of Mount Tenjo. When you depart Kouzushima for Tokyo, you will be able to see the other side of Mount Tenjo with the Kouzushima village as well as the various Izu islands.

We stayed at the Yamashita Ryokan (山下旅館本館) - a traditional Japanese ryokan in an old building with shared bathroom and toilet facilities in the middle of the Kouzushima village. Complimentary return airport transfers were provided as part of our stay. Do note that there is another Yamashita Ryokan Bekkan (Annex) located near the beaches. Wi-Fi and ensuite toilet are only available in the Annex and not at this ryokan in the village.

The dinner and breakfast included as part of your stay at the ryokan, are one of the best Japanese meals I have tried - there was a sumptuous feast of seafood delicacies and vegetable dishes. Dinner was ready at around 6.30pm.

After checking in at Yamashita Ryokan, we began our sightseeing at the island with a chartered taxi service (8 hours for 15,000 Yen - about 150 USD). We drove to the southern end of the island to hike along a trail which would bring us to the Kouzu Lighthouse and Senryoike lake (千両池). Do note that you will need to walk up quite a number of steps up a hill to reach the lighthouse.

The next part of this trail leads to the Senryoike (which means secret) lake which is a crater filled with sea water. You can also enjoy a picturesque view of the seas around Kouzushima. During summer, this is a great spot for swimming and snorkelling as this crater is sheltered from the rough sea waves.
Unlike the trail leading to the lighthouse, the path to reach the lake is less well defined - there are spots where you will need to pull yourself up rocks using ropes.

Our next stop was at the Arima Observatory (ありま展望台) which is also the location of the Julia's Cross - a monument to Julia Otaa and other Christians who were exiled to Kouzushima during the 17th century.

This observatory offers views of the Kouzushima village and the port and on a clear day, you can even see Mount Fuji and the Japan mainland across the sea.

For lunch, we had buckwheat soba at Maitory - a small restaurant in the Kouzushima village known for its handmade buckwheat soba noodles.
I strongly recommend the duck buckwheat soba noodles (1500 Yen) - the duck meat was tender and the soup was very savoury (dip the cold soba noodles into the soup for the best taste).

After lunch, we drove to the eastern side of the island to the Miura Observatory which overlooks the Miura Bay. There are a lot of good scuba diving spots around the island and the sea around Miura Bay is one of the more popular one. With the clear water, you can see a wide variety of temperate and tropical marine creatures during your dive e.g. colourful tropical fish, coral reefs, sea turtles, dolphins and sometimes even sperm whales.
The Miura observatory offers excellent views of sunrise over the Pacific Ocean and the 2 islands on the horizon - Miyakejima and Mikurajima.

At the Tako beach, there is a spot where the natural spring water flowing from Mount Tenjo is collected. You can take a sip or fill your water bottle with the freshest spring water which beats any mineral water hands-down.

Tako beach is also a very beautiful beach with the clearest waters around it due to the white sands. The sand is white because of the erosion from the Mount Tenjo cliffs. What makes this beach very interesting is that it is peppered with dried up carcasses of pufferfish - according to locals, this is a lower grade of pufferfish that fishermen would dispose of. Even birds do not like to eat the fish.

At Tako Bay, you will also find a lot of fishing boats bringing in their catch for the day. If you enjoy fishing, you can also charter a fishing boat out to the sea. You can also fish off the port like what most locals do.
The Kimedai fish (金目鯛) is one of the most caught fish in the sea around the island and is a Kouzushima delicacy so you can try it in many restaurants, cafes and ryokans in the island.

The Akasaki walking trail (赤崎遊歩道) on the northern end of the island is a popular tourist attraction in Kouzushima. The clear and calm waters make this place a perfect spot for swimming and snorkelling.
In the summer, you will find a lot of people swimming and snorkelling in the area and jumping off the white wooden platform and surrounding cliffs into the water for a swim.

After a long day of hiking and sightseeing, we decided to wind down with a relaxing hot spring onsen experience at the Kouzushima Recreation Center (Kouzushima Onsen Hoyou Center).For the outdoor onsen, you are required to wear swimwear as both male and female bathers can use the onsen together. You can enjoy great views of the sea and the strong waves as it crashes on the cliffs and rocks around the outdoor onsen.

We started off Day 2 with a trek to Mount Tenjo. There are 2 ways to get to the top of Mount Tenjo:
The toughest way for experienced and fit trekkers is via the 黒島登山 (Kuroshima Tozanguchi). This is a steeper and longer route and you should set aside about 6 to 7 hours to complete the trek
The easier way for trekkers who are less fit and do not exercise regularly is via the 白島登山 (Shiroshima Tozanguchi). This route brings you to the summit (最高地点) of Mount Tenjo faster. Most people trek to the trailhead (i.e. starting point of the trail) of either黒島登山 or白島登山 by foot all the way from the Kouzushima village. However, if you do not have time (e.g. your flight back to Tokyo departs in the afternoon) or is not fit enough to walk all the way to the trailhead, you can hire a taxi to bring you to the trailhead from the village. It will be based on metered fare - the estimated fare is about 3480 Yen (about 35 USD). There is a toilet at the entrance of the 白島登山 trailhead - do go for it as there won't be any toilets at the summit. Also, if you need help, grab walking sticks from the basket at the trailhead before you go up.

What is unique about Mount Tenjo is the almost 360 degree scenery view of the ocean and the Izu islands you can enjoy from the summit, the beautiful wildflowers that bloom all year round (these flowers typically grow at an altitude of 2000 metres but they can still be found at the 574 metres Mount Tenjo).

The trek to the summit is only half of the journey. To explore the volcanic crater lakes and deserts at Mount Tenjo, trekkers will need to do a round loop around the summit. Do note that while on the map below, it looks like a plateau, the trekking path is not an easy one to take and part of the trail require you to pass through narrow paths lined with prickly and thorny bushes and manage steep inclined paths with loose rocks.

360 degree viewpoints at the Tenku no oka (天空の丘) where you can get a view of the Izu islands around Kouzushima and even Mount Fuji on a clear day and …

you will reach the Fudo-ike (不動池) which is an interesting stop. Here you will find a heart shaped pond with a bridge to a shrine for Ryujin, the dragon god (the pond was dried out as we took this trek during the dry season). There are also some benches for you to rest or have lunch (you will need to bring your own food) …

Eating where the locals eat is usually a safe bet that the food is good and affordable. We stopped at Yochare Center for lunch which is a busy restaurant filled with locals, mostly workers from the nearby harbour. The set meals are all 1000 Yen from sashimi rice set to curry fish set and pork chop set and you order using a vending machine (though it is all in Japanese - ask the staff if you need help). The set meal also includes the Ashitaba tempura - Ashitaba is a local produce at Kouzushima and you should try it at least once when you are here.

I love Japanese snacks e.g. Tokyo Banana and Hokkaido chocolate and I will buy a bunch of them back home whenever I visit Japan. Kouzushima also sells Kouzushima-only snacks i.e. snacks made with local produce like Ashitaba and passionfruit. If you are interested in getting them, buy them in the island as I have not seen these snacks sold elsewhere in Tokyo. There are 2 souvenir shops I know of on the island and both are located side by side near the only traffic light on the island.
Besides snacks, you can also get magnets, T-shirts and other Kouzushima souvenir. Do take note that your baggage allowance for your flight back to Tokyo is only 5 kg and you will be charged excess baggage of 300 Yen per kg if you exceed the 5kg limit so you have to plan your shopping.