I don't have the largest wrist either for someone 6'2", but I wear different styles of watches depending on what the occasion is.
The typical Rolex face is not all that large. Brietling and Tag Heuer tend to have a larger diameter and look better with suits.
For running around in the summer, a sports watch always works fine. I like watches and collect a few of the nice ones and have some cheapos that look like art, just for fun.
If you have a smaller wrist and want to wear a watch, I recommend a Skagen, since they have a really LOW profile and very thin.
They make sense on a small male wrist. Affordable, yet still unique. http://www.skagen.com/us/en/men/products/watches.html