From Narita Airport, Enoshima is reachable in as little as 2 hours if you're lucky to catch a Narita Express limited express train that travels to Ofuna station (¥4500). From Ofuna, Enoshima is 15 minutes away on the Shonan Monorail (¥300).
From Haneda Airport you will have to take at least three lines: The Keikyu Line to Yokohama, the JR Tokaido Line to Ofuna, and the Shonan Monorail to Enoshima. Costing ¥1060, this will get you to Enoshima in one hour with good connections.
You can take the private Odakyu line from Shinjuku to Fujisawa (54 minutes via kaisoku-kyūkō (快速急行) or 66 minutes via kyūkō (急行)), then change onto the rattling old Enoden (江ノ電) half-train/half-streetcar line to Enoshima. The Enoshima-Kamakura Free Pass (¥1,430) will get you a roundtrip from Shinjuku and unlimited use of the Enoden line for one day.
If you don't want to experience the vintage Enoden, you also have the option of taking the Odakyu all the way to Katase-Enoshima (片瀬江ノ島) station, which is the closest location to the main beaches and the island of Enoshima. There are not too many direct trains from Shinjuku; however, a connection at Sagami-Ono or Fujisawa is easy and convenient (you walk about 10m to the other side of the platform).
For a small extra charge you can take the all-reserved limited express "Romance Car" train direct from Shinjuku to Katase-Enoshima. The service to Enoshima is called, appropriately, Enoshima (えのしま), with some weekday services from Shinjuku also known as Home Way (ホームウェイ). Be warned that many of these trains are coupled to services bound for Hakone, which split at Sagami-Ono. There are more Romance Car trains to and from Enoshima on weekends and holidays than there are on weekdays.
The one-way fare from Shinjuku to Katase-Enoshima on the Odakyu Line is ¥1210 for the Romance Car, and ¥610 for regular services. Users of the above-mentioned free pass can upgrade to the Romance Car for ¥600 each way.
If you have a Japan Rail Pass, you can reach Fujisawa by taking a Tokaido Line from Tokyo (about 50 minutes) or a Shonan-Shinjuku line train from Shinjuku (about 50 minutes) at no charge, then pay the fee for the Enoden. A better, faster and more exciting way is to take the Tokaido or Shonan Shinjuku Line and change in Ofuna (大船）to the Shonan Monorail （湘南モノレール）, one of the few hanging monorails, that will take you directly to Enoshima（湘南江ノ島）in about 20 min. They don't accept Suica/Pasmo, so you have to buy a ticket.
Most places in Enoshima are easily reachable on foot. However, there are high slopes and hills in Enoshima. It will be hard to get around on foot for elderly. In that case, you better take an Escalator called Enoshima Escar for easier trip. It costs only ¥ 400 for a day, open 9:00~17:00.
Enoshima's many sights are concentrated on the island of Enoshima itself, in front of the beach and the modern town. Enoshima is blessed with the abundant beauty of nature and sea.
The shrines at the top of Enoshima 2 chome have an all seeing turtle painted on the ceiling.
The Points located on the backside of Enoshima near the cave are a sight worth seeing. Tidal pools brim with crabs and trapped fish. The backside of Enoshima is the local fishing secret.
Lovers Bell at the park in 2 chome.
You can see fireworks in summer at the beach. Every year, about 5,000 fireworks are displayed in late July or in early August. A local radio station announcer will be hosting the display. Many small booths would be lined up on the streets and you can get food and drinks on that day.
There is also the Enoshima Aquarium (江ノ島水族館 Enoshima-suizokukan). The aquarium has a decent collection of marine life, and you can see some poor dolphins do some tricks in a very small pool. However, you can expect the aquarium to be very crowded on hot summer days!
Enoshima is all about sea sports, particularly surfing. The surf here isn't actually great by most standards, but it's conveniently close to Tokyo and provides an excuse to strut about with an artificial tan, bleached hair and a surfboard under your arm.
Enoshima has a big yacht harbor. Many cruisers are docked there and many university clubs that have their boats. Recently, a sailing Olympic week was held there.
The small island of Enoshima is attached to the mainland by a causeway, and during low tide you can walk there on exposed sandbars. In addition to the marina there is a small temple and a modern observation tower on the top of the island. If you are not in great shape for the climb, escalators are available for a fee.
Nature and animals are abundant on the island. The classic view of Mt. Fuji as depicted in Japenese art can be seen from Enoshima on clear days. Giant hawks called tombe fill the skies, squawking and diving.
The island is surrounded by high sea cliffs, rocks and tidal pools. The pounding surf and rocks make swimming at the island rather suicidal but many people walk across the exposed rocks, exploring the tidal pools and crab pots. Access is on the cliff side of the seawall behind the marina or by going over the top of the island. Both routes are exclusive of each other (see below). If you don't mind getting your feet wet you can (at low tide) go around the island from the side of the causeway opposite the marina and return over the top.
The street that leads from the Enoden and Monorail Station to the beach has souvenir shops and surfer accessories shops. In the same street you will find a Natural Lawson convenience store.
The street on the island that leads up to the shrine has also the typical souvenir shops, but the real specialities can be found right when you leave the bridge: grilled and fresh seafood in every variation is sold there. It's a bit like the Tokyo fishmarket in small if you look at all those creatures that can apparently be eaten.
Many visitors come to Enoshima to eat seafood. One of the famous dishes is called shirasu-don. It is a small fish which is raw placed on top of a bowl of rice, with soy sauce is poured on top. The turban shell, or sazae, is also popular. Reasonably priced (by Japan/Tokyo/beachfront standards) meals are readily available at the many beach houses in the summer, but these places are disassembled promptly at the beginning of September.
The area also has purple soft-serve ice cream (often sweet potato or sakura-flavored), and usually there are dozens of different soft-serve flavors you'll never see in the United States among the many different shops on the island.
Enjoy a cold one during the summer months at one of the many beach houses.
Enoshima is an easy day trip from the Tokyo/Yokohama area, but an assortment of hotels are available in the beach area. However, most of them are hotels for couples, calls "Love Hotel" in Japan, so you need some courage to get in there by yourself.