If you're going to run your headphones unamped, you should look at headphones with low impedance. As you've noticed, Grados are easy to drive. That's because their drivers have only 32 ohms of resistance. If you're not amping, you'll want to stay away from headphones that have much higher impedance, such as 300-ohm Sennheisers.
Ironically, I was going to suggest you look at Sennheiser, which has a "house sound" that is more polite. Some would say it's "more refined," but I think it's really just more "laid back." Sennheisers typically roll-off the upper-mids and low treble. This means you can crank them louder and not feel overstimulated by the treble. The problem is that many Sennheisers have a higher impedance.
If you like the Grados but find the SR80s just too bright, there are Grados that have a mellower response. The SR80s have a reputation, even among Grados, of being a bit bright. I loved mine but I know exactly what you're talking about. There are ways to tweak your SR80s to mellow them out - short of having to buy a new pair of headphones - but if you're not interested in changing or modifying your existing headphones, there are better choices, even from among Grados. The Alessandro MS1 is the rough equivalent of the SR125. Many like both cans better than the SR80. Among the lower-priced Grados, the SR225 is considered the best choice by far. My favorite is the HF2, which is extremely mellow. It has plenty of thump and a restrained high-end, enough to make it a killer can for rock.