How to improve face that are printed on support? Is there anything I can do to improve the bottom side of surfaces that are printed on support?

I always try to rotate the model so that surfaces that need to look nice are on the sides or top, and, if possible I divide the model into smaller parts to minimize the amount of support.

But sometimes there is an object that has an irregular shape that need support no matter how I rotate it and can't be broken down into smaller objects with no support.

And then, after removing the support I get a very ugly ridged face that takes forever to sand.

To clarify, I'm not asking about making supports easier to remove, I don't have a problem with this, I'm talking about making the surface that touched the support better looking after removing the support.

Is there anything I can do to improve the look of the face that is printed on supports?

I'm using Cura to do the slicing and printing, I'm using the "lines" support type, my printer is the Robo3D R1+
The basic answer to your question is to create better bridging or overhangs on your machine. Bridging is when you are printing between two solid pieces (like a bridge). Overhangs occur when printing off of a single solid piece and coming back. Most slicing engines allow extra settings for speed, fan power, etc for these parameters, just refer to this terminology.

A very common and simple solution in getting features to 3D print properly is to just slow down! If you're not a in a rush to get the part done, you bring down all of the feedrates in your slicing engine. MakerWare has mine at 90/150 mm/s for print and rapid. Typically I'll bring that down to about 50/90. My reasoning is the more time you give the plastic to cool, both while and after printing the layer, the more rigid that layer will be for the next one. When briding or overhanging, there will typically be a sagged area in the print. You can minimize this by providing the plastic more time to cool. Also keep in mind that printing on supports is still technically bridging (printing between two solid pieces).

Another thing to keep in mind is adhesion from one layer to the next matter just as much between the current layer and the previous as the current strand to the one next to it. So, in some cases, increasing your shell could possibly make it easier for the infill/roof/floor strands.