I think we can make an educated, intelligent guess as to where Jesus was when the word came to him from Bethany that Lazarus was ill.
First, we know that when Jesus received the word from Bethany that his friend Lazarus was ill, Jesus and his disciples were somewhere in Perea, engaging in what scholars call--fittingly enough--his Perean Ministry. They were there because Jesus chose to retreat from the volatile religious/political atmosphere which existed in Jerusalem because of his repeated claim to be the Son of God (see John 10:22-39). Knowing that the time was not right for his "departure" at Jerusalem, he eluded the Jews who attempted to seize him (10:39) and traveled east, "beyond the Jordan" (10:40) and into Perea.
We do know that Perea, part of the tetrarchy of Herod Antipas, was an expanse of land, east of the Jordan River. It was approximately 20 miles wide and 60 miles long. It extended from its northernmost boundary in northwestern Decapolis, to its southernmost boundary where the Arnon River (i.e., Wadi Mojib) empties into the eastern side the Dead Sea.
As you pointed out, Jesus was "staying" where John the Baptist had first baptized penitents (John 10:40). Perhaps it was also where Jesus himself was baptized by John. For the sake of argument, let us assume the two locations were one and the same.
This web site suggests that Jesus' baptism was located about five miles north of where the Jordan empties into the Dead Sea. Evidently, a number of ancient churches were built there because of the area's connection to Jesus' baptism by John, and their remains have been unearthed in recent years by archeologists. From this site to Bethany, then, could have been a day's journey on foot, or about 15 miles.
Putting together two facts from the biblical narrative (viz., Jesus stayed where he was for two days after having received news of Lazarus's illness, and Lazarus had been dead four days--according to Martha--when Jesus gave the order for the stone to be removed from the entrance to Lazarus's tomb), we can reasonably conclude a couple things.
First, Lazarus may have been dead for one day when word from Bethany arrived "beyond the Jordan" with the news of Lazarus's illness. Second, Jesus and his disciples did not leave immediately for Bethany, for 11:6 tells us,
"So when [Jesus] heard that [Lazarus] was sick, he then stayed two days longer in the place where he was."
Third, when Jesus arrived at the tomb of Lazarus, Lazarus would indeed have been dead four days. The arithmetic is as follows:
One day for word of Lazarus's condition to arrive where Jesus and his disciples were in Perea. Lazarus dies at approximately the same time Jesus is told Lazarus is ill.
Two days for Jesus and his disciples stay where they were.
One day for Jesus and company to travel back to Bethany in Judea.
For a total of four days from the time Lazarus died to the time Jesus stood near the tomb and cried out with a loud voice, "Lazarus, come forth" (11:43).
This scenario is not necessarily the only possible scenario, but it is one which makes sense, given the information we have in John 11 and 12.
In conclusion, Jesus and his disciples were likely at the place where at least one tradition puts him when word came to him from Bethany that his friend Lazarus was ill. That place was beyond the Jordan, approximately 6-8 miles due west of Jericho, where John was first baptizing and where John may also have baptized his Lord, and it was also approximately 15 miles from Bethany.