For those using public transport, bus is the most convenient way to get to Donghae for most people. The bus terminal is a 20 minute walk north of the downtown area (5 minute cab ride.) There are frequent buses to the Express Bus Terminal in Seoul (takes a little over 3 hours), and less frequent buses to Dong Seoul (East Seoul.) There are also buses leaving every 10 minutes for Gangneung (35-40 minutes) as well as buses to most other cities in Gangwon Province. There are 3 overnight buses to Busan.
The Yeongdong line goes through Donghae, stopping at Donghae Station (south of downtown) and Mukho Station (north of downtown.) There aren't a lot of trains, however, and those there are don't go to too many places that are appealing to tourists, making the bus more convenient for most tourists.
Donghae serves as the main access point to Ulleungdo, with regular ferry service throughout the year (usually once or twice a day in each direction, more frequent in the summer.) Ferries leave from Mukho Port, a 5 minute drive north of downtown.
Mureung Valley (무릉계곡)
This is a fantastic valley with several hikes of varying difficulties. You can hike to waterfalls, temples or up mountains. Admission to the valley is 1,500 won for adults. The valley can be reached by taking any of the city buses numbered 12-something (e.g. 12-4.) The bus fare is 1,000 won.
Popular beach area 7 or 8 km north of town. Very crowded in the summer, with a very small amusement park area with a batting cage and a few rides.
Donghae has limited food options but "Soma" is quite good. there are actually 2 locations located about a block away. They offer Korean food with a slight western twist (like pizza ddockboki and pork cutlet with pepper sauce), worth a try. The fast food options are limited to KFC, Dunkin Donuts and Lotteria (the Korean McDonalds). They have good pizza at Buena Pizza (try the bacon cheeseburger). Of course, there are the ubiquitous galbi and kimbab restaurants. However, those hoping for authentic western food may be disappointed.
LOVE MOTELS As with everywhere else in Korea, love motels abound and Donghae is no exception. Don't be fooled by the name however, some of them can be seedy, however some can be quite special with huge beds and themed kitsch. Try the hotel "very six". A room with a pool table can be had for 90,000 won. Most rooms go for 50,000 won a night (more on weekends).
JimJilBang(짐질방) Donghae has a few of these as well. You can sleep in them for W6,000 a night (give or take). However its a communal experience and those looking for privacy won't find it here. For those that are willing to try a more authentic Korean experience, they are clean, safe and really cheap. The one close to the very six hotel is the best in town (near E-MART)