The Poskim discuss whether it is permitted to wear a watch on Shabbat in a public domain without an Eruv. All agree that it is prohibited to carry a pocket watch. Even if it is gold plated and attached with a gold chain, it is not considered a Tachshit (jewelry), as the watch itself is concealed in the pocket. Therefore, Hacham Ovadia (Yehaveh Da’at Vol. 3) and the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) in Siman 301 rule that it is forbidden.
The major Halachic question is with regard to wristwatches. The general principle states that only an item considered a Malbush (garment) or a Tachshit (jewelry) may be carried into the public domain. The definition of a garment is an accessory worn to protect or cover the body. According to this, a wristwatch is certainly not a "Malbush." Hacham Ben Sion (Or Le’sion vol. 2) and Hacham Ovadia do not consider a wristwatch in and of itself a Tachshit. They write that if the watch would be transformed into jewelry with a gold or silver band, it could be permitted, since it would cease to be merely a functional item.
The Menuhat Ahaba (Rabbi Moshe Halevi, Israel, 1961-2001), in his comprehensive treatment of this question takes a different approach. He grants that the watch is not considered a Malbush or a Tachsit. Nevertheless, he argues to be lenient, comparing it to Tefilin. In principle, it is permitted to wear Tefilin in the public domain, even though they are neither a Malbush nor a Tachsit. The reason is that anything that is normally worn during the week in that fashion, may also be worn on Shabbat. He applies the same logic to wristwatches and rules that they are permitted. He also brings a proof from the Halacha that a prisoner is allowed to wear his shackles in the public domain, even though they are neither a Malbush nor a Tachshit. Rather, since that is what he wears during the week, he can also wear it on Shabbat. His leniency would therefore include all watches, not just ornamental watches. Rav Moshe Feinstein, the Magen Ba’adi, as well as Rabbi Yeshaya Dayan (The Av Bet Din of Halab) concur with this position.
The lenient position seems to be contradicted by the ruling of the Shulhan Aruch, which states that it is prohibited to wear a functional item, such as a key, even after being transformed into an ornament. Why would an ornamental watch be different from the key? Hacham Ovadia deals with this difficulty and suggests that the watch is more of a garment than a key pin. Hacham Moshe Halevi differentiates by saying that the watch, as opposed to the key, can be used even while being worn.
Interestingly, even the poskim who are lenient, conclude their treatment of the subject by saying that those who refrain from wearing wristwatches are praiseworthy. However, those who do wear a wristwatch in the public domain have what to rely on, especially if there is a "quasi-Eruv," which they do not usually use, and the watch is ornamental or stylish.
One may be lenient and wear a wristwatch in the public domain on Shabbat, especially if there is some type of Eruv and the watch is ornamental or stylish.