The Edinburgh City Centre HIEx is a very good one for an Express standard (the rooms are fine and it has quite a good bar, which also sells meals if required, although there's plenty of restaurants nearby). It's about 10 to 15 minutes walk from Waverley train station. One thing to bear in mind is that Edinburgh counts as a special destination and so unfortunately it's 20K for a reward night rather than the usual 10K.

The Crowne Plaza (on the Royal Mile) left the IHG portfolio a couple of years ago (it's now a Radisson).

You can get to Carnoustie by train (there are quite a few each day) from Waverley, which takes between 1.46hrs to 2.06hrs, however you'll need to change trains at Dundee. Check out this Trainline website for your required travel details. I hope this info helps.