I have a Trek Pilot 5.0 and before I lowered and rotated the handlebars it was quite upright. I also saw a woman with a Trek Pilot 1.2 today that had even taller handlebars. It was very upright, but still had the drops for multiple hand positions. I'd say the stem was a good three or four inches higher than the seat. A bike shop might be able to do that for you.

I'd also check out some touring bikes like the LHT from Surly.

If I were doing long rides, I'd worry about being able to have multiple hand positions. Flat handle bar bikes don't really allow for that.