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.
Highway 65 ends in Donghae and connects the city to Gangneung further north. From Seoul take highway 50 to Gangneung which then leads to the 65. South Korea uses a toll system for their inter-provincial highways. Seoul to Donghae costs W11,400 one way in tolls. However if you are a group of people (at least 3) driving is a cheaper option than the bus. The trip from Seoul takes about 3 hours when there is no traffic.
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.
E-MART is the only big chain retailer in town. They offer everything from food to clothes and electronics (think wal-mart). Apart form them, there are a number of shops in the downtown area offering your usual services. English will be limited however and bargaining is not too common in the retail stores.
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.
Most of the options here are Hof and Soju bars that are all pretty much the same - they offer beer by the truckload (w2500 for 500ml) and soju. Many of them will expect you to order food as well since this is Korean tradition. Just politely say "no thanks" and most will leave you with you beer. Those looking for cocktails have to go to a cocktail bar and these are priced very highly. Your best bet is to head to E-Mart and get a few bottles of cheap booze if you want liquor.