We visited the following sites on or near the Sea of Galilee:
Tiberias, Mount of Beatitudes, Capernaum, Sea of Galilee, Jesus Boat.

We spent two nights in Tiberias and it marked the end of our boat trip on the Sea of Galilee but we didn't do any serious sight seeing in the city.

The Catholic church has built a beautiful church at the site where it is believed Jesus gave the beatitudes as found in Matthew 5:1-12. We had a nice devotional service while visiting the site.

Other sites: Bible Places and Bible Walks. The first includes pictures of a field where Jesus may have given the sermon.

After Jesus was attacked in Nazareth, he made Capernaum his home base for at least the first part of his ministry. At the time he lived there, it was an important town as it was on a key highway and had a customs house and military guard post. It was a busy fishing town.

The remains of a very nice synagogue have been found there. It is generally believed that it was built in the 2nd or 3rd century and replaced the synagogue that Jesus taught in. Franciscans purchased the site in 1894 and partially restored this synagogue.

Another reason why Capernaum is important to Christians is it is assumed to be the home of fishermen Peter, Andrew, James, John and even tax collector Matthew. A particular home was revered as Peter's home since late in the 1st century AD. It has been rebuilt a few times and today there is an octagonal Catholic church built on pilers above the home believed to be Peter's.

Today, in addition to the Catholic church over Peter's home, there is a nearby Greek Orthodox church at Capernaum.

A couple of sites where you can learn more about Capernaum: Wikipedia and Bible Places

The Sea of Galilee is actually a fresh water lake on the Jordan River. It is about 13 miles long and 8 miles wide. At about 700 feet below sea level, it is the lowest fresh water lake in the world. Today the Israelis take water from the lake to be used for irrigation.

In the New Testament, it is sometimes called Lake Galilee, Lake Tiberias or Sea of Tiberias (John 6:1), or Lake Galilee or Lake Tiberias, or Lake of Gennesaret (Luke 5:1) or Sea of Gennesaret depending on the translation. In the Old Testament it was called Sea of Chinnereth" (or spelled as "Kinnereth") (Numbers 34:11; Joshua 13:27).

In Jesus day, it was an important place for fishing. 1st century historian Josephus reported 230 boats regularly worked on the lake. The lake and its shores were sites of much of his teaching and many of his miracles. For example, it is believed that the Sermon was given on its shores (Matthew 5-7, Luke 6::20-26). Sometimes the wind whips across the lake and Jesus calmed the storm on this lake that frightened his fishermen disciples (Matthew 8:23-27, Mark 4:35-41, and Luke 8: 22-25) . He walked on its waters (Matthew 14:22-32, Mark 6:45-56, and John 6:16-21). He lived on its shores in Capernaum at the beginning of his ministry. He fed 5000 people on its shores (Matthew 14:15-21, Mark 6:30-44, Luke 9:12-17, and John 6:6-13). He helped his disciples catch a large number of fish (Luke 5:1-11 and John 21:1 -11. In John 21:11 it says they caught 153 fish. In Hebrew, 153 would be written in letters that spell "I am God"). There were other events on its shores that are too numerous to mention here.

For more information about the Sea of Galilee, one can consult these links: Wikipedia and Bible Places