Especially, a man should be careful not to go out with a ring on which there is no engraved seal, and he should certainly not wear a watch, even if it is attached to a gold chain that he wears around his neck, which is an ornament. A pocket-watch is certainly considered a burden, and is not permitted. [Footnote #6: Some are lenient regarding the ring, as with other jewelry (See MBY 303:18 Women’s jewelry today - part 1), but a pious man should not go out of the eruv wearing any ring. See Mishnah Berura 303:65.]
[Ed: As the issue of jewelry – especially as it relates to a man – is of halachic complexity, let us quote a relevant excerpt from The 39 Melachos, by Rabbi Dovid Ribiat, (Vol. IV - p. 1360)]:
“To be halachically classified as jewelry (Ed: i.e. and thereby not subject to the Torah prohibition of carrying outside of an Eruv), the item must be designed and worn for the primary purpose of enhancing the wearer’s personal appearance or the garment he is wearing. Examples: Earrings, bracelets, brooches, pendants, dentures, etc. are permitted because they enhance the wearer’s appearance. A feather in a man’s hat, a decorative handkerchief in the outer breast pocket of a jacket, or a badge or medal of honor pinned to his shirt or jacket are all permitted, because they serve to enhance the appearance of the garment.
However, if it primarily functional (or even just equally functional) for other purposes as well, it can no longer be classified as jewelry, but rather as a functional utensil. As such, it cannot be considered subordinate to, or part of, the person, even though he is wearing it. Therefore, wearing such items is ‘hotza’ah’.
1) Primarily functional: a pocket-watch or (according to some poskim) a simple, unadorned wrist watch, a name-tag pinned to a jacket or worn around one’s wrist, a brass key.
2) Dually functional and ornamental: a plain watch hanging from a necklace (even if the necklace is gold), a key attached to a bracelet, a silver key adapted as a tie pin (according to some views).”
(Ed: As stated, these halachos are complex, and there are differing opinions. One should consult his Rav when questions arise. Of course, none of this is relevant to an area which is circumscribed by an Eruv.)