Where John was baptising

John 1.28  This all happened at Bethany on the other side of the Jordan, where John was baptizing.

The introduction to John the baptiser in the narrative proper of John's Gospel situates us in a place with two descriptions.

1. Bethany
2. On the other side of the Jordan

However there is a problem with this. He is either in Bethany, or he is on the other side of the Jordan. We know from John 11.18 that Bethany is a couple of clicks away from Jerusalem (literally 15 stadia, which works out to 5km), and is on the same side of the Jordan.
So he could be there, except the rest of John 1-2 situates us in Galilee; he meets his first disciples by the sea of Galilee, he goes to a wedding in Galilee, he 'goes down' to Capernaum in Galilee and so on.
Furthermore, at the end of the 'Book of Signs' (the first half of John), Jesus is at the place where John had been baptising (10.40) and takes several days to walk to Bethany (11.17).
How do we solve all this?
D. A. Carson (The Gospel According to John, Pillar New Testament Commentary. Grand Rapids: Eerdmans, 1991, pp 146-7) suggests that John (the author) has deliberately misspelled a region in Israel's north-east called Batanea (Βετανια) as Bethany (Βηθανια). Batanea is in Galilee, it is across the Jordan, it is pretty wild, and it is several days walk from Bethany.
Currently this area is in the Golan Heights, an area of Syria occupied by Israel for the last couple of decades.

Arik Bridge over the Jordan River. Photo by Ilya Viten (Google Maps)

Why would he do this?

1. The words sound quite similar - it's only two letters - 'ηθ' (ith) rather than 'ατ' (at).
2. There's a nice symmetry to the book - the first half of the book begins and ends at Bethany/Batanea, with Jesus being recognised there at the beginning, and then performing his greatest sign at the end - the raising of Lazarus.

Andreas J. Köstenberger (John, Baker Exegetical Commentary on the New Testament. Grand Rapids: Baker Academic, 2004, pp 65-66) explains further:

At Bethany in the (Galilean) north, John the Baptist confesses Jesus as “God’s lamb”; at Bethany in the (Judean) south, Jesus nears his crucifixion. 

In conclusion, it's possible, though not provable, that when John wrote about John baptising Bethany in Galilee on the other side of the Jordan, he was expecting his readers to know that he was discussing Batanea, but drawing a strong link to Bethany. As readers we should be drawing those links too - from the beginning to the end.