Search "Hotels, Denver".
How are we to know what you want?
The only "Nice, romantic" hotel I know of is the Brown Palace, but it's hardly affordable.
See, that's the problem. You want nice, you have to pay for it, you want affordable, you get less.
I doubt you're going to find a hotel with a fireplace in the room, or if you do, that would allow you to use it...cause, you know, at 95 degrees or so in July, you're not going to want to start a fire in the fireplace!
I also doubt there are any "cabins" in Denver....it's kinda...you know...a big city.