I found this list of 12 for a visual artist tour on the Visit Britain site and it looks fabulous:
1. Tate Modern, London. 2. Chapter Arts Centre, Cardiff. 3. The Lighthouse, Glasgow. 4. Yorkshire Sculpture Park, West Bretton, West Yorkshire. 5. St. Ives, Cornwall. 6. National Gallery, London. 7. The Lowry, Manchester. 8. The National Museum, Cardiff. 9. Turner Contemporary, Margate, Kent. 10. Open Eye Gallery, Liverpool. 11. Jupiter Artland, Edinburgh. 12. The Hepworth Wakefield, Wakefield, Yorkshire.
Looking on maps I discovered that the Hepworth Wakefield and Yorkshire Sculpture Park are very near to each other and could done in a day. Except for the 2 Cardiffs and 2 Londons: the rest are pretty much far spread. From what I was reading these are all considered world class and feature modern to contemporary besides some classic collections. Does anyone have a favorite they would like to add?