The types of schedules and what your day looks like is as varied as anything else. I must disagree with wtb, as there are plenty of jobs out there, that are in hospitals, that do not have call. While I have not sought those out, it is really all I have ever known. There are night shift CRNA's. They work full time. My current job is in a huge, university hospital, and there are two CRNA's who split the nights. No call for anyone. Simple fact is, every single hospital, job, and group, will do their schedule a bit different. But if not taking overnight call is important to you, you should not have too much trouble finding a job like that.
Keep in mind, however, that everything is a tradeoff. With no call may come less pay, less flexibility, less variety of cases, etc. There are very, very few perfect jobs out there. Just have to prioritize.