Barnes & Noble deleted the Browser on the Nook,
so don't even think about that...
Although you can root the Nook and install a browser, I believe.
The Kindle has a decent browser (for an e-ink) but it can freeze up if the page is too complex. Mobile-optimized websites should work fine on it, though. The few sites I have browsed on my Kindle Touch (like wikipedia) have been very snappy if they were mobile-optimized.
The Kobo has a browser, but I don't have one so I don't know how good it is. It is probably just about as good.