so many........ to count few:
1) Near Wat Isan temple.
2) The big river on Buriram-Prakhon Chai road (Road 219) may be an interesting option.
3) Ban Samet have big river there.
4) Ban Prasat near Wat Kradun Thon have big river there. (Road 219, Buriram-Satuk).
5) Satuek have huge river there, you may want to try, I think it has an ideal location, facilities like the park beside the river and have good breeze there.
6) Ban Kok Lek (Near Ban Yang village,Buriram).
AND MORE....
Basically, almost every village have a local lake where there are wild or less wild fishes..
I'm not sure which place it is allowed to fish or not, I think the locals fishing in places it is not permitted also so you need to check it as well, just take a tour there and see if you are welcome to sit there and fishing, usually will have some groups fishing already in places where it is allowed.
Bring a case of cool beers and I'm sure you will find lots of friends.