It's a great trip, but you need to time your visit to the tides or you'll regret it. My wife studied Old Germanic languages, so a visit to Holy Isle was a must-do. We stayed in a nearby inn so we could leave when the tide was running out.
If you're in the north-east of England it's absolutely a wonderful thing to do.
Lindisfarne was the beginning of a long distance walk on St. Oswald's Way connecting to a section of Hadrian's Wall. Fascinating part of the country although the section from the mainland from Lindisfarne back to the coast is one of the less interesting.
We just walked along the causeway. The timing with the tides was a bit tight when we were there and it made more sense to take the more straightforward route although it wasn't as "authentic" as taking the path through the tidal flats.
If you're in the north-east of England it's absolutely a wonderful thing to do.