<p>I'm attaching a picture to show my issue. I'm hoping might be an easy settings fix, or at least maybe someone has a couple suggestions I can try. I'm using an Ender 3, and the program Cura. The print on the left was printed with the opening facing up. The print on the right with the hole facing down. The support leaves a rough surface. Any suggestions for support settings would be appreciated. <a href="https://i.stack.imgur.com/AnkLP.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/AnkLP.jpg" alt="enter image description here" /></a></p>

There's only so much you can do about this without a multi-material printer that can utilize dissolvable material or material that doesn't bond to the print material, and print the supports at zero distance from the model. So expect it to be ugly. But not quite that ugly.
Slicers, including Cura, have options to control the Z distance between the support material and your model, among other things. Reducing this will make it harder to remove the supports, but will give a better bottom surface. It only really works on whole-layer granularity in Cura (while some other slicers let you do arbitrary distances), and really should always be equal to one layer. A distance of two or more layers will give really bad results, which might be what you're seeing.
Also, Cura has an option called "support interface", which you want on. This prints a flat top surface on top of the support, below your print, so that all the lines of the print have something they're resting on. Without this, the bottom surface over the support will sag down between the lines of the support and look very bad - or, if it's a small detail, it might sink entirely between lines of the support and effectively not be supported at all!
Finally, one hack you can try if you don't have a multi-material printer but want to try printing supports at zero distance from your model: set support Z distance to zero and use a slicer plugin to pause-at-height just past the top surface of the support. Then, when the printer pauses, paint a release agent that won't bond to the print material on top of the support. Reportedly Sharpie permanent markers work as such a release agent, but I haven't tried this, and there are probably better choices.