Here's two of my favorites, Ohthere and Wulfstan. These travelers visited the court of King Alfred the Great in England, probably around the year 890. Alfred had someone working on translating a book from Latin into Old English, and the book had a long section on geography, so the scribe simply copied in what he learned from these two travelers' accounts. Ohthere was a Norwegian who had sailed north for fifteen days and probably rounded Scandinavia into the White Sea. He also sailed south to the trading town of Hedeby at the base of Denmark.

That's where Wulfstan's account picks up. Wulfstan was probably an Englishman, based on his name, and he had traveled east from Hedeby to a town called Truso, near modern Gdansk, Poland. Ohthere's account is unique as a very early account of what seems to be exploration for the sake of exploration. Wulfstan's account is surprising because he was an Englishman sailing into the heart of viking territory at the height of the Viking Age.

I'm also a big fan of Ibn Fadlan's account of his travels north. He was an Arab diplomat and explorer who in the 920s traveled through Central Asia and into modern Russia. The Viking Answer Lady has posted his descriptions of the Rus', that is, the Norse merchants and thugs who had moved in to dominate the Russian river ways. His account is harder to make sense of, since some of it seems like tight-lipped reporting of things that he genuinely disapproved of, but other bits of it seem to be pure flights of fancy.

There was actually a blossoming travel literature during much of the middle ages, although many of these works were either the travelogues of pilgrims or propaganda works promoting the cults of saintly missionaries. Ansgar, a missionary bishop to Denmark and Sweden in the 830s is a personal favorite. So is Egeria, a German woman who traveled to Jerusalem in the 380s. Willibald, an Anglo-Saxon pilgrim who made it to the Middle East in the 720s (perhaps the first Englishman to do so), is also fun. I'm not sure if these accounts fall squarely within your idea of 'solo explorers,' however.