Mile redemptions are priced by region, so there's not really going to be a lowest cost routing, except "whatever the computer comes up with." Just put in CTG and ORD for your travel dates, and if any "saver" awards come up, those are the lowest cost routing. For business or first class redemptions, flights on United are cheaper than partner airlines -- that's really the only routing rule that comes into play. For economy, it's all the same.

As for purchased tickets -- in general, routing isn't a primary concern for finding low fares. Any difference in fares for published routings is going to be due either to inventory concerns or to airport taxes / fees for your intermediate airports.

I put in a couple of sample dates, and the cheapest UA fare I see has the routing rule CTG-SAL/BOG/PTY-HOU/EWR-CHI. A '/' means a choice, and a '-' means a transfer; all transfers are optional. So, you could fly CTG-SAL-IAH-ORD or CTG-PTY-ORD or... etc. All would be the same price, plus or minus the various airport fees.

In practice, you're more likely to find fare variations based on the destination, day of week, season, or inventory level than the routing. In addition to Google Flights, try matrix.itasoftware.com . It's by the same people, but it sometimes shows you a lot more options. It also has a calendar view that can be helpful if you're flexible.

Hope this helps.