The two stand out bouldering walls in Scotland are Eden Rock in Edinburgh and the TCA Newsroom in Glasgow. If you don't have a car then Alien Block in Edinburgh is another good option, Eden is a bit of a trek on public transport but 2x the size of Alien. There's also a newer wall TCA Propstore in Glasgow that I've not tried yet but think it's smaller than the Newsroom.
For roped climbing EICA Ratho is world class, but the bouldering is limited.
The outdoor bouldering in Central Scotland isn't that great. There's some at Dumbarton but better for people who are already climbing hard stuff outdoors. Most people would go south to Northumbria or north into the Highlands. In the Highlands hillwalking/scrambling can be a better option than outdoor bouldering because you keep moving (which means you don't get surrounded by midges) and a little bit of rain doesn't stop you.