In Llandrindod Wells, there is a delightful little museum, housed in the 'Automobile Palace', ironically yet appropriately once you know the history. They have the most magnificent collection of bikes and trikes, going right back into history, and pretty much up to the present day.
There's a good display on Eileen Sheridan's career, and a lot of documents about Flying Gates (a perverse passion of mine).
The only downside is that the limited space means the bikes are packed pretty close together, and the photos behind can be a bit hard to see. Nonetheless, there were enough items of interest to my avelopic (but nostalgic) parents that they didn't get bored while I wandered round taking loads of photos.
If I go again, I shall make sure I leave at least an extra hour on top...
More hereMuseum website