I don't live at CT but I can give some insight. Roughly 40% of the class lives there first year as it is directly across the street from campus. Its dog friendly (KCUMB has a community garden and dog park next to it), cheap, and has a gym, common areas, parking etc. Its basically a mid level apt building with a dorm like feel to it. Perfect if you like to be close to school and want to be around your fellow students. The downsides are that there isn't much you can walk to around campus, and you're around med students 24/7 haha. A lot of students live there first year to meet people and then move somewhere nicer. If you interview here you will have an opportunity to tour CT and get rental info.
The rest of the class is pretty spread out, people live anywhere from 3 mins to 1 hour away from campus. River Market and Downtown KC have a lot of options and both are around 5mins from campus. They also offer plenty of stuff in walking distance, places to run, etc. Many of the buildings are nice and have great amenities. There is also Westport (10 minutes from campus) with lots of bars, restaurants, etc, and The Plaza (15 minutes from campus) which is a modern, hip are with lots of shops, bars, restaurants. Most of the River Market/Downtown/Plaza places are more money than CT but you get what you pay for with amenities like covered parking, pool, gym, etc.
If city living isn't your thing there are plenty of apartment complexes out in the suburbs that have decent amenities, are a bit quieter, and are only 10-20 minutes from campus. Some students also choose to buy or rent houses just outside the city, might be a good option if you have a family and intend to stay in KC for rotations and beyond.