Hey guys, welcome to columbia!
I'd like to point out that Columbia isnt that large of a town so you aren't likely to every be more than 20 minutes out from campus. And that's like being out in really rural areas. My husband and I lived off route K which is what providence turns into if you go south enough and our drive to campus was about 15 mintues. I'm not off Providence on the norht end of town, same deal. There is a lot of student housing south on Providence and off Nifong, though this is mostly undergrad from what I understand so I'm not sure that it is exactly family friendly. The town is full of duplexes though, and finding somewhere to rent really shoulnd't be a problem. Columbia doesn't really have a *bad* area of town per say though some neighborhoods around Hickman are a little more sketchy than you'd expect. Even those aren't bad compared to some bigger places.
Ms. Kate is great and Dr. Early is great for mamas too. I love how they are two sisters, one NP and one doc. Just seems like a great family atmosphere. My kids aren't vaxxed and we didn't do well baby stuff so I don't get to see them very much but every time I've needed them, they've been great.