There is a wharf at Lyness. I can't say that you could definitely tie up there, but as I understand it, many of the dive boats tie up for an hour between dives, so maybe you can. You can see it, though not very well, behind the guy's head in this picture.

The museum is well worth a visit. My missis was in tears at some of the stories. Stromness museum is more of a general maritime museum, and we spent a couple of hours in there. They even had a sabre from a chap who sailed with Bligh on the Bounty. Marvellous, if you like anything to do with the sea.
There is a small set of pontoons at Stromness, and we saw a couple of yachts having great sailing.
We really fancied the Orkneys as an area to sail - it was so calm, even with F6 and F7. There looked to be lots of places you could anchor, and I'd love to visit some of the beaches on the outside of the islands. The one we saw at Skara Brae looked stunning.