I would also recommend the Big Horns... With all the areas I suggest, you are going to have to keep in mind that Wyoming weather is extremely unpredictable. Especially in October... so it is going to be kind of hit or miss depending on that.
Unit 45- Is an awesome area. There are a lot of elk in there. There are no grizzlies here. In all honesty, you are going to have wolves just about anywhere you go now. But Area 45, there is not an abundance of them. The terrain is a little difficult in places, but a little nicer compaired to some of the other areas in the Big Horns. If they get a bunch of snow around that time, the elk will be down low and the valley over there is pretty easy to hike around with kids and such. I have taken my 6 year old there.
Unit 38- This is the area that I generally hunt. It is a very good area for archery. I have heard that rifle tags also rock for this area but have never drawn one myself because I always put in for archery only. This area can eat you alive if you let it. The terrain is pretty intense... especially if you want to get off the beaten path and actually get into elk. But there are normally a really good number of elk in here.
Unit 37- Definitely a hit or miss area... There are a lot of people with success here. It is a general, over the counter tag for Wyoming residents and so you will have a lot of people hunting this area also. But as long as you are willing to work a little for it and hike, I think you would have good luck here.
This is purely my opinion... I'm sure some other people that live in the area might think differently than I do. This is just my experience. If you have any questions, feel free to message me.