Where exactly did Boromir's journey take him?

In my Lord of the Rings journey video I plotted Boromir's journey as best I could. However, there are a lot of constraints on his journey and it's kind of a puzzle to find the exact path.

We know all of the following things:

• When the journey started and ended.
• He got a horse at Edoras, likely spent some time there, and then lost his horse at Tharbad. Not sure if he definitely had a horse from Minas Tirith, but I assume he did.
• He hadn't seen Hobbits before when he met Frodo, so he may or may not have gone to Bree on his journey, depending on how many Hobbits hang out there. I assumed he didn't make it to Bree.
• He didn't start out knowing where Rivendell was. He wandered somewhere, but there are actually not that many places he could have wandered to while still keeping to his known schedule.

Any other details we know that tell us precisely where his journey took him?