There's Cathedral Peak from the hotel and also The Rhino from Garden Castle. Both are longish days at get you up to 3000m. And both are excellent hikes worth doing in their own right.
Not sure about any long-lasting altitude benefits though. To acclimatise, you'd have to spend a few days on top, the benefits would wear off soon after the trip and wouldn't help much for 5895m

It may help to get a feel for how your body reacts to moderate altitude? I certainly notice a whole lot more huffing and puffing when slogging up those escarpment hills for the first day or two of an overnight hike!