We have a few days in Sorrento and want to spend one walking the path
of gods and one going to the Blue Grotto.
Just to comment on this....
If you mean the Blue Grotto on Capri, there is no dedicated walking path the grotto: you'd walk vehicle roads from Anacapri to get there, and it will take an hour or so. You are also not allowed to swim in it during the hours the boats are operating, and it's not safe to do so at all when the seas are rough.
https://www.capri.net/en/s/la-grotta-azzurra
"Can visitors swim in the Blue Grotto Capri?
No, visitors can neither enter the cave by swimming nor disembark from
their rowboat to swim inside the cave. However, after the cave closes
to the public at 5:30 p.m. (when the rowboats and ticket office
close), many swimmers enter the cave by sea. This is both illegal and
dangerous, as the cave mouth is low and narrow and in case of high
waves it is easy to get thrown against the rocks."
Just thought that was worth mention if walking there during the day to swim was your plan? IMHO, we've hiked some of the island and that isn't one I'd choose if only having one day. You might look at Villa Jovis, Pizzolungo (both of which we've done) or take the chairlift up Mt. Solaro from Anacapri and hike down to Capri.
https://www.capri.net/en/traveller-search?todo%5B%5D=nature&all=1
(you do not need tours for any of this)
