Akko is old. Very old. It was inhabited without interruption for over 4000 years. It did get destroyed and rebuilt a few times but it still feels that old. It reminds me a bit of the medina of Marrakech, with the same maze of narrow alleys and markets, except better maintained and cleaner.
The main attraction is the crusader citadel, built by Templar Knights 800 years ago. It's a large complex with huge vaulted halls, courtyards, and an entire underground city, all very well maintained with only a few gaps filled in with modern materials. They really make you feel like the knights might walk in and sit down in the huge dining hall any moment. There is also an old Turkish bathhouse, the Hammam al-Pasha, a forgettable modern museum and an intriguing historical museum in the city wall that packs more artifacts per square meter than any other museum I have been to, arranged in historical workshops. Akko also has a delightful old port.
Saturday in Israel is the Shabbat, where everything shuts down, even public transport and most restaurants. Not so in the old town of Akko because it's 90% Muslim. Getting back to Tel Aviv was also easy - trains and buses are out, but large taxi vans, Sheruts, still operate. My connection in Haifa was seamless, the drivers are happy to help. During the hour-long drive from Haifa to Tel Aviv I had to sit on the floor though; demand for Sheruts is high on Shabbat.