One solution that comes to mind for me would be a combination of plugins rather than just one. My way of thinking this:

Form plugin that has the ability to select dates, times, location – just about any typical form plugin would do. There are paid ones that may handle that better. May need to do some research on that one.

Plugin that could accept payment. There are tons and tons of those available and each form building plugin usually has some extensions available for that as well.