There are at last count, seven courses in St Andrews. The old course is pretty busy.

http://www.standrews.org.uk/welcome/st_andrews_links_trust/interactive_links_map.html

This lists the main 6.

you can book online from the main page.

This link lists some courses in FIFE all within about 25 miles of St A's

http://www.standrews.org.uk/your_visit/golf_courses_in_fife/index.html

If this doesnt take your fancy there is always Carnoustie, another Open venue, about 15 miles away.

You will never be short of a round of golf in this part of the world.

Cant stand the game myself though.