A chapel is any place where religious services can take place. So for example the little room set aside in an airport is a chapel, cos obviously the terminal building isn't actually a church! At Glasgow Uni there's a catholic
chaplaincy with a mini halls of residence, some meeting rooms, a refectory etc and a
chapel - again the building isn't a church but there's a room reserved for worship, with an altar etc.
As spoonie says, ideally the word "church" refers to the people, but in practice it means the big stone place where they meet too. Often a church building will have a small area denoted as a chapel - if the design of the main church space is in the shape of a cucifix, as many are, the area that sticks out to the right (as you face the front) of the central aisle (or "nave") will often be a chapel. (
diagram here - numbered 13)
And yeah, midnight "masses" (usually that term is used for both the whole service and the sacrement of holy communion by Catholics; other (protestant) Christians don't use the word much except for this one christmas service!) are usually something like 11:30pm on Christmas
eve til just after midnight - but if you're feeling a need for a bit of religion then you'd be welcome at any church at any time, don't feel you can't go just cos you missed this one opportunity that most people take to pop into a place they otherwise wouldn't go!
In general churches have their main services on sunday mornings and evenings but many do have a brief service eg every morning or lunchtime to fit around people's work schedules - that church at Nelson Mandela Place next to Buchanan St underground has a service every day at like 12:45-13:15 so people can go in their lunch hour; glasgow uni chapel has one daily from 8:30-8:50 so students can get their fix of God before lectures (or before exams they haven't studied for, perhaps

)
So yeah, there's lots of opportunities; I sense that you're not entirely committed to a particular denomination so it shouldn't much matter where you go.