St Andrews only has one cinema, the New Picture House. Always popular, it shows a mixture of blockbuster, mainstream and some arthouse releases. NPH also hosts late night showings of previously released films at 11pm on a Wednesday night. The programme is here: http://www.nphcinema.co.uk/index.html
There are large multiplex cinemas in Dundee -
Cineworld: http://www.cineworld.co.uk/cinemas/19
Odeon: http://www.odeon.co.uk/fanatic/cinema_information/s86/
Alternatively, you could visit Dundee Contemporary Arts. This arthouse cinema shows a wide range of films, as well as live screenings from the likes of the National Theatre and the Met Opera House: http://www.dca.org.uk/. On top of that, DCA also hosts a variety of workshops, exhibitions, talks and events.
If your taste for film is still not satisfied, the Edinburgh International Film Festival takes place in Edinburgh each June. Now in its 65th year, the festival runs a vibrant programme of films and events.