It all depends on what you're looking for in terms of what to include or not include about the stair-climbing experience. If it's things like the stairwells themselves, there are machines ranging from the omnipresent StairMaster to Stepmills. If you're looking to avoid machines and stairwells, there's also simple box routines. Put a box out. Step up on it. Step down. Repeat ad nauseam. That will get you some similar benefits in terms of building your leg muscles and cardio-vascular health without putting you on actual stairs or hitting the gym. If it's the resistance of lifting your body, bicycles exercise some of the same muscles and will help with the cardio.
If it's just the monotony of the stairs, I'd advise doing something to break up that monotony. Music can help. Some people have no problem reading or listening to a book while doing the stair-climbing. And, of course, there's always doing variations such as skipping steps whether going up or down, hopping up and down the steps, or changing your body orientation while traversing them (these, of course, start to shade into changing your type of exercise entirely, especially if you get into more exotic variations such as quadrupedal movement up and down stairs, head up or down).
