Stayed at Highland Country Inn just over a year ago. Was clean and neat. I don't think there was any interference from the trains (cheap places in flag are usually right next to the tracks, the I-40 "trap").
"It's only when you stand over it, you know, when you physically stand over the bike, that then you say 'hey, I don't have much stand over height', you know"-T. Ellsworth
The Roadway Inn Downtown Flagstaff is pretty cheap and just a block or two from the heart of downtown. You can ride from the hotel to the trails (Schultz Creek or Buffalo Park Trailheads) making for a nice warm-up. Rooms are pretty small though you would have a hard time getting more than 2 bikes in a room.
I have a car. I made a choice. I ride my bike.