I guess what you call "barge" is the Gabarre.
Several short excursions (about 1 hour) in gabarres are possible from Domme.
"Les Gabarres Norbert" located in La Roque-Gageac, 10 minutes from Domme:
https://www.gabarres.com/?lang=en
"The Barges of Beynac"
Located in Beynac-et-Cazenac, 20 minutes from Domme:
https://www.gabarre-beynac.com/
(website in French only)
There is a lot to see in the Dordogne. Here is an area located about 75 km northeast of Domme where several unmissable places are close to each other:
Collonges-la Rouge, classified as one of the most beautiful villages in France.
https://www.visit-dordogne-valley.co.uk/discover/cultural-heritage/villages-to-visit/collonges-la-rouge
Very close to Collonges, the castle of Turenne: also classified as one of the most beautiful villages in France.
https://www.visit-dordogne-valley.co.uk/discover/cultural-heritage/villages-to-visit/turenne
15 minutes by car from Collonges: the medieval village of Curemonte, one of the most beautiful villages in France again!
https://www.visit-dordogne-valley.co.uk/discover/cultural-heritage/villages-to-visit/curemonte
On the road to Collonge-Turenne- Curemonte , you can stop at Martel, a village dating from the 12th century (and come say hello if I'm around):
https://www.visit-dordogne-valley.co.uk/discover/cultural-heritage/villages-to-visit/martel
And of course, the very famous and touristic Rocamadour, Sarlat la Caneda, etc.
About things to eat, the region is known for its black truffles, everything made from duck: confit, foie gras, duck breast...etc.
There are also many nut producers.