Vinh's role as an industrial port city led to heavy destruction by aerial bombing during the war. As a result it has remained a drab, rather uninteresting place. However, there are some sights around such as some old citadel gates and a square which can be seen. It also makes for a good pitstop for the train journey between Hue and Hanoi as there is a recreation centre near the train station which provides some leisure activities.
The train line between Vinh and Dong Hoi to the south takes an inland route different from Hwy 1. There is some excellent scenery along the way. If you're travelling along the coast by bus, consider taking a break here and going by train. There are trains daily from Hanoi to Vinh.
Vinh bus station is available (https://goo.gl/maps/oDxXTLxrhZ12) but there does not seem to be information on the public bus routes. Otherwise, walking, taxi and Grab / Uber are available as always.
There are three old citadel gates: the front gate (https://goo.gl/maps/PkJvDwWBPHH2), the left gate (https://goo.gl/maps/SgD44rv1ExC2) and the right gate (https://goo.gl/maps/BwUPGgi61ip). There are some informational plaques at the gates which are only in Vietnamese. The gates are marked with signs in Chinese (前门, 左门, 右门).
Ho Chi Minh Square (https://goo.gl/maps/VCDyi1nnYox) has a statue of Ho Chi Minh and a fountain.
Ho Chi Minh's childhood home, Hoàng Xuân Đường, is some distance away (http://maps.google.com/?cid=8490193175479364799&hl=en&gl=gb).
Pù Mát national park is also in the vicinity of Vinh (https://goo.gl/maps/KPbQFwx4AP62).
Vinh Recreation Centre (https://goo.gl/maps/xb3gcuGfAh42) has an indoor pool, cinema, gym, children's playground, arcade and karaoke machine.
There is a tour agency which sells some tours in Vinh (http://vinhguru.com).
There are small shops and convenience stores dotted around. The Vinh Train Station Market, Chợ Ga Vinh (https://goo.gl/maps/1G18J9hMXfF2) is near the station as well as Vinh Recreation Centre and has various stalls.
Vinh Recreation Centre (https://goo.gl/maps/xb3gcuGfAh42) has a Breadtalk, King BBQ (Korean BBQ) and Highlands Coffee.
Chao Luon (the local specialty of eel porridge) may be found at various roadside stalls or small eateries.
Banh Muot (rice rolls with fried onion and Vietnamese pate) may be found at roadside stalls.
Apart from Highlands Coffee at Vinh Recreation Centre (https://goo.gl/maps/xb3gcuGfAh42), there are numerous coffee and beer shops dotting the city, as with most other cities in Vietnam.
There are several Khách Sạn (hotels) near the train station.
Bus to Phong Savanh (Phonsavan) Laos, with visa available at border. The bus leaves every second day at 06:00.