My cross bike is pictured below (the Fuji), and I love it and use it for those kinds of trips. It came stock with 700x32 tires which weren't bad for riding on the street (I wore them out and have since switched to 700x34 for racing cross). I do have a second, lighter wheelset with a wider range cassette as the cross bike doesn't have as wide of a range of gears for climbing as I'd like on the road (I'm in Colorado). Dh and I rode the Mickelson Trail in South Dakota earlier this year, and it was perfect for that. I highly suggest a cross bike - mine has done everything I've needed it to without having to get another bike; I have done well in triathlons and am a group ride leader on road rides by simply switching out my wheelset to the slick tires.