Gator, He asked about the Black Hills, not West River. Did you miss that?? He also said that he was looking for Mule Deer because they have Whiteys where they live. Geeze bud, It wasn't like I was calling your mama ugly, just the Black Hills mule deer. Look at the stats, 21 mule deer with 5 or more points per side (4 point with eyegaurd) were taken from the sample of 2150 hunters. That is a less than 1% chance of shooting a mature mule deer in the Black Hills.
3d- I think you could have a good time in the Black Hills archery hunting. Just don't expect a lot of mature mule deer. There are over 2 million public acres there and much of it is very dense. Could be good for a bowhunter, but I have not been in there in Oct. Sounds like you and your family have a good attitude and would have a good time, so why not give it a go. Licenses are cheap enough. Another option would be a Utah archery hunt in August. Lots of public land, lots of National Parks, a better chance at seeing mature deer, lots of other wildlife to view (elk in pre-rut), and it is only another 10 hours in the car with the kids.
Now if you are from South Dakota, have family which still lives there, can get a West River tag, and hunt on private property with a rifle you could probably harvest spindly horned 22" 4 points (with the occasional 170 buck). hahaha