Where is the most convenient place to stay in Columbia from the trail? Wanting to avoid too many hills or a lot of traffic. Any suggestions?

This subject has been commented on a few times. here is what I wrote a month or so ago to another rider who wanted to avoid the streets and traffic when staying over night in Columbia, MO.
If you'd like to stay at Stoney Creek Inn, you can ride the trail all the way there until you get to Old Route K (at Epple Field) and go south about 4/10 of a mile and you are there, no need to get on the street except for that 4/10th of a mile, but just know you will probably walk it, as it is a about a 20% incline or upslope.
You can take the Columbia MKT to the MU Recreation Trail and the first street you come to is Old Route K (aka Old Providence Rd).
You will see the MU Rec Trail Between the Forum and Stadium Trail Heads in Columbia.
Also, if you click on Columbia at the top of this page, it will show you a map of the Columbia MKT Trail, which is an extension of the Katy Trail. It has mile markers and you can print out the map to take along with you on your ride. Also, while on the Columbia page, there is other info and hotel info that can be of help to you.
If you do go to the Columbia page there is a long comment from Barry, I think, that covered him asking about staying in Columbia, also. Read his question and all of the comments and I think it will help you alot.
Have a good ride!

On the first trip we made to Columbia we stayed out by I70 which meant hills, traffic on Stadium Blvd, etc.

On the second trip, I stayed at the Hampton Inn on the south east side of the MU campus. I got off at Flat Branch Park and cut across campus without hills and traffic. There are restaurants/bars, etc. on the north edge of campus and there is a restaurant next to the Hampton also.

Also, to add on to Trek's comment. Hinkson Creek Trail that goes by Epple Rec Field also goes over to Capen Park and Rock Quarry Rd and is just 2 blocks from Hampton Inn at Fellows Place (Stadium Rd and Rock Quarry Rd), so you can stay on the trail to get to the Hampton Inn as well.