Get out of the temporary railway station, walk east to Qingnian Road, then walk south along Qingnian Road to West Street, and then walk east along West Street to Tonghui Hotel. The five-room Koreatown is located on First Avenue in the south of Tonghui Hotel.
Although it's a long way, there seems to be no direct bus, so taking a taxi will start at a price.
If you insist on taking the bus, the 4 1 road should be the nearest. Yantai Science and Technology Market seems to be only one stop from Yantai Bus Station.
Koreatown's things are still quite distinctive, and the things are OK, both fine and cheap.
I have been to Jinan before, and there is no concentrated place with Korean characteristics.
The bus station is nearby, and there are hotels everywhere. If you want good quality and low price, there is a Rujia in the west of the bus station, and there is a good Korean restaurant with oxtail soup below Rujia.
You have many questions, but they are all easy to answer. Have a good time in Yantai.