This is a good one if you’re feeling like a few more miles. Taking in fantastic views on both sides of the Tay if you do the loop or either side if you’re going one way only. https://www.strava.com/routes/4810370
This would also be a good route from St Andrews giving you a get out if the weathers bad and if the weather’s good then you can stop for a bite in Ceres which is a very nice little place to rest tired legs. https://www.strava.com/routes/4810504
Hopefully the links work.
Be aware that the road from St Andrews to Leuchars is pretty miserable to cycle due to it being winding and busy. I’d avoid it. There is a cycle path that goes beside it but personally I’d rather ride on quite roads rather than next to a busy one. I live only a few miles from St Andrews so if you want any other ideas of where might be good just let me know.