Given the purpose of your trip, let me recommend that you take a look at this book, https://www.amazon.com/Golf-Scotland...allan+ferguson. By the time I read it, I had taken several trips to Scotland. Two things: many matters he covers, I can corroborate through the experiences I'd already had; second, the things I didn't know, especially the bits about checking clubs to see if they're running open competitions while you're there and the multiple ways to get on the Old Course, were extremely helpful.

If you're going during the summer, for relatively low cost but convenient lodgings in St. Andrews, consider student housing at the University. There are some dorm facilities at the Agnes Blackadder Hall located off the main road leading out of town towards Leuchars that splits the St. Andrews golf courses and the more modern parts of the University. Not luxurious, certainly, but you'll get a double bed with an ensuite shower plus a free breakfast plus laundry facilities plus free wifi for approximately $80 per night for a solo. These rates appear to hold for the stretch during the Open at Carnoustie next summer. Short walk to the Old Course and surrounding pubs and restaurants but far enough away from the action so that you won't hear any noise. More info: https://ace.st-andrews.ac.uk/accommo...ackadder-hall/.

Dundee is fine, but St. Andrews is a unique experience for a golfer. After playing a round there, you'll want to hang in the pubs located near the R&A without having to drive back to Dundee. And there's plenty more to do there, including sightseeing at the ruins of the St. Andrews Cathedral, the British Golf Museum, and the ancient Castle.