Start with the GFP Website and look up previous years reports, areas of bird numbers and harvest, hunter pressure, etc. The areas with the highest bird numbers and easiest access will have the most hunters. Easiest access would be anything within a certain area of I-90. Communities with the most hunters would be Sioux Falls, Mitchell, Chamberlain, Pierre, Mobridge, Aberdeen, and a few others. There's also a reason why those areas have hunters that continually come back, there's usually birds. However, you can find birds anywhere depending on how hard you work and a bit of luck. The NE part of the state is more prairie potholes, cattails, sloughs, and less birds - but they are still there. The Missouri River corridor holds birds on both sides of the river and will be some of the best hunting there is, but it is also a lot of valleys and wiley birds that flush ahead. The SC part of the state has started to become my go to, lots of land and weekdays I don't run into much for hunting pressure. The SE part of the state also holds birds.
I like to be productive and not waste my time in areas that don't look birdy. A birdy area to me has a food source in a nearby field - especially a picked a corn field that still has the stocks and not turned over to a black sea yet. A nearby water source. A nearby shelter belt or tree line. A nearby cattail or warm cover area. A nearby prairie or loafing area. Sometimes all of this is found on the same piece of public land. Sometimes the public land has the hunting opportunity for me, the neighboring private land provides some of the other resources that lets me know it should at least be a birdy area. A lot of times if it does not have all or most of those, I skip it.
Read through the rule book and understand what a Right of Way is. Don't overlook ditch hunting. There are some very minimum maintenance roads, that are hardly even roads anymore that can provide great hunting. When walking ditches, again I like to be effecient. I look for good grass that is on both sides of the road so I can walk one side down and the other side back. I want a picked cornfield with stubble on at least one side, not a bare pasture. If it has a lower wet area that has a cattails somewhere along it, there's usually where the birds are. The birds like to run before flying, so keep an eye out for the things that are going to make them stop running and fly - crossroads, narrowing of ditch, etc.
SD birds are smart, especially late season. They are old dogs that have seen all the tricks. Show them new tricks. Park in a different area than others have parked all year. Approach them from the direction that you think others have not (but still play the wind, if you think that helps your dog). Don't slam your car doors when you pull in. Don't sound the horn on your car when you lock it in the parking lot. Don't walk in a straight line, zig zag. Try to use non-verbal cues to your dog or fellow hunter.
I started SD public land in 2009 and through trial and error, lots of learning, and taking notes, I have seen my success rate increase drastically over time. That said, I have had trips where I've hardly gotten bird and had trips where I've gotten a fairly easy limit. In my opinion, any group of 1-3 hunters can reasonably expect to get a limit on SD public land every day. Now everybody has a different definition of what you can reasonably expect - if you get a shot, don't miss, you might not get many other chances when your goal is a limit. Good weather, good dog work, being in the right area at the right time. And hunting hard, go the places where others won't. For me, I'm young and in shape, if that means walking a half mile through marginal cover because I see an area of good cover where out there that I think most people will avoid - I'll go hunt it and usually have success. Look for the "spot within the spot". The endless sea of prairie holds birds, but they often run or flush wild ahead. Look for the spot within that spot that is different somehow - different type of grass, tree line, thickets, brush, water, low area, slough, etc.
I know that it is fun to sleep in in the morning, but don't be afraid to use that (late) 10am start time to scout. Drive around and make a plan for the day. Cross off spots on the map that don't look birdy, circle the areas that do and that you'd like to come back to. I'm all for supporting your local cafe for lunch, but in December the days are short and you want to maximize the time in the field. If you hunt a spot from 10-11:30 or noon, drive to the next town and eat lunch, then get back in the field, before you know it is already 1:30 and you only have 3.5 hours of daylight left. Hunt hard, don't waste time, pack a lunch.