There is a very evocative description of Elrond in chapter 3, when Bilbo and his company arrive at the Last Homely House, Elrond's residence at Rivendell.
Elrond is described as being exemplary in numerous ways, being as "fair in face" as an elf-lord, wise like a wizard, venerable like a dwarf-king, as strong as any warrior, and "as kind as summer"—which Tolkien gives last in his list, as if to indicate that this is the most important thing about Elrond and the resounding impression with which Bilbo is left. Elrond and his house are a matched pair: in the house, no matter what kind of person you are, you feel refreshed and renewed. Tolkien states that not only clothes and bruises were tended to and fixed at Rivendell, but also "tempers and hopes."
Elrond is somebody who has been a fixture in many stories in Middle Earth, and his house has heard many tales and welcomed many travelers. Gandalf is already very familiar with him. Elrond is very old, but at the same time he is ageless; he has a great and very useful knowledge of almost everything, specifically maps and runes.