I've been to Tangier a few times, as we further inland. For a day trip to Tangier the shortest crossing on the fast boat from Tarifa (~30min), though you can also sail from Algeciras (1.5hrs). Make sure you get the right ferry. Some ferries from Algeciras run to Tangier Med, a new ferry port which is in the middle of nowhere half way between Tangier and Ceuta. FRS Iberia run a fast ferry from Tarifa to Tangier, and Balearia from Algerciras to Tangier proper.
Arrving in Tangier main port you are right in the town itself, which centres around the harbour. It's easy to explore by foot so you dont really need an organised tour, and it's a nice place just to wander around, rather than visit any "must do" sites. The old Hotel Continental is a wonderful old-world European colonial style hotel near the old Medina at Rue Dar el-Baroud, a short walk from the port. It's well worth seeing and perhaps stopping for a drink.
I guess the city is an aquired taste, and if it's your first time in Morocco it's pretty manic and overwhelming, perhaps a bit intimidating. But ignore the touts, stick by the rule that anything that seems to be good to be true definitely is, then you won't come too unstuck, and will get to see a really interesting, lively town that can be a fun place for a day out. If it gets a bit much just head into one of the western hotels for a drink on their terrances, and if you want to go back home, it might feel exotic and far away, but it's just a case of jumping on the ferry.