Ian,
access should not be an issue at all. Possibly Muirfield might be an issue and if you want to play there I would suggest writing to the secretary asking for their advice on the matter. TOC is as Ash says, just rock up early morning and check in with the starter who should have no problem getting you in a group within the first couple of hours. At most other places I would just write well in advance.
As much as I would like to suggest staying at my wife's guest house and using it as a base to explore the likes of Dornoch, Tain, Brora, Castle Stuart, Nairn, Moray, etc...... and some of the great second tier clubs such as The Boat, Fortrose, Golspie, Elgin, Nairn Dunbar, Wick..... for the ultimate first time experience of Scottish golf if you can find yourself accommodation in the middle of St. Andrews and play ALL the links trust courses, plus Elie, Scotscraig, Leven links.... then you just cannot go wrong.
Jon