I'll arbitrarily decide that by "relatively budget", you might be thinking $100 or so. It's been a while since i filled this niche in my collection, but if I was shopping today I'd be looking at the Sennheiser HD 4.40. I keep seeing them on sale for about $100, and I'd probably bite.
On-ears predominate in this price range, so it's a bit tough to find good over ears from a reputable maker. If your budget increases, your options get wider. Avoid the off-brand over-ears that you find everywhere. Rare gems, lots of junk.
A couple of flyers on discontinued items if you can find them - the Mee AirFi Matrix 2 with an HM5 pad mod was great for well under $100. The Parrot Zik 2.0 can also be found for less than $100. Nice sound, a design you'll either love or hate, but poor battery life (by no means pay more than $100). I still use the Mee regularly, and my wife loves her Zik 2.