Ann, I considered the Billy Shiel tour also, but I was there about 3 weeks ago, and the tour doesn't start until May. One advantage you have to taking the tour is that it arrives at high tide, which means it may be less crowded.
I highly recommend seeing the Priory and the museum, St Mary’s Church, which is the oldest building on the island and includes sections from the Saxon period and Lindisfarne Mead (you can try the free samples). You might want to skip the castle, if you're running low on time, although it's interesting to look at from the outside. It's actually a 16th century fortress that was converted to a holiday home for a millionaire. I'm not sure about the Gertrude Jekyll gardens. When I was there, there was not much blooming but that may have changed in 3 weeks.
ETA: Also, there is an interesting excavation site of a church from the 9th century that may have been St. Cuthbert's original grave (unlike what the priory says). It is up on the hill above the priory. Just follow the coastal path and you'll come to it. It was discovered a few years ago and it sits in a gorgeous spot, with beautiful views of the sea, castle and coast.
BTW, while I was there, I found St. Cuthbert’s Center, which is a great place to go if you need a toilet or free wifi. Seriously, it’s a lovely little building managed by the United Reformed Church on Holy Island. Not every building has a toilet (as I found out), so it was a great place for that, and just sit for a while and relax. Everyone is welcome. I was the only one there when I walked it and it was a very comfortable place. It's right next to Lindisfarne Mead.
