That Phanom is a little of a one-attraction town, but it's a nice enough place to spend a day or so. If you're just passing through Nakhon Phanom province on your way somewhere else and have a night to kill, you might be better spending it in That Phanom rather than Nakhon Phanom city, which is just an hour or less away.
The main attraction in That Phanom is the tall spire known as Phra That Phanom, which is the center of a temple just a short walk from the Mekong riverfront. Between the temple and the river is a traffic circle with a sort of triumphal arch in it, and between this and the river are some old, mostly run-down, shop-houses that can be worth a stroll.
A road runs along the river. On one side, on the banks of the Mekong, are several restaurants serving fresh-water fish from the river, and there's also a stretch of promenade. The inland side of the road is lined with a few hotels and guest-houses. At the north end of the riverfront area is the small temple of Wat Hua Wiang, which has an ordination hall decorated with some unusual murals.
Other places of possible interest include the city's main market, just southeast of the That Phanom temple, and a night market with lots of food which is set up every evening along the road running up the east side of the long lakes which stretch north of the temple. You'll find deep-fried frogs and other local 'delicacies'.
That Phanom is small enough that you'll have no problem getting around it on foot, but if you should need them, there are many tuk-tuks that can take you where you want to go.