I would highly recommend going to Buffalo Springs National Reserve! There were so many breathtaking moments during our long weekend there that it exceeded my expectations. Most notably, there were so many elephants in the park that at one point our car was in the middle of a very large herd (more than 100 elephants) walking past. It will be one of my best memories from all the national parks!
At another point, we came around a corner and saw a small family of elephants right next to the car. There were several baby elephants and one of them pretended to attack (it was playing, the mother remained calm - making noises, running towards the car with ears out). It was the cutest! We stayed with the family for some time and saw the baby elephants feeding, trying to throw dirt on themselves like the mothers etc.
The roads are not as good as in some other National Parks (ex Amboseli where you have proper flat roads) but I only appreciated that because it made it feel more natural. Even though we had a 4WD, there were some parts of the park where we could not drive and needed to turn back. In either case, I would recommend paying to go on a game drive. We did both (i.e. self-drive and game drive) and not only were we able to go to parts of the park that we could not go on our own, the experience was much better with a game drive as the driver was able to find spots and animals that we could not have found on our own.
Buffalo Springs actually does have a spring (not just a name) where you can go swimming. We brought towels from the hotel one evening and went for a swim - it was a nice experience and rather warm water. Even though I didn't try it, I would recommend going to the spring towards the evening since I assume that several game drives go past the spring during the day. When we were there we had it all for ourselves, could not even see a car around.
Several of the lodges are located along the river (recommended) which means that animals usually come very close to the lodge. Where we were staying, we could sit on our balcony and see several elephants walk past just a few meters away.