Shabbos (or Shabbat, depending on your dialect of Hebrew) should not be spent alone. It is not forbidden, but Shabbos should be a happy time, spent with friends and family. And there are thousands of Jews all over the world who love to have Shabbos guests, either for the entire Shabbos, which includes sleeping and meals, or just for meals. Whatever works for you.
Shabbat.com is a site devoted to bringing Jews together for Shabbos. It is widely used, and I highly recommend it.
There is also Oneg-Shabbat (which means “Shabbat Delight”), dedicated to “putting you in touch with families and new friends wishing to host a Shabbat guest.” I don’t know anything about the site or the people.
To find a Rabbi or a synagogue, visit one of the following sites, and conduct a search.
Orthodox Union Synagogue Network
This search engine does not find all synagogues in an area; it has only a small percentage. However, some of them seem to be synagogues you might not find on most other lists.
A vast list of synaogues all over the world. This list looks like it’s almost a complete list.
This is actually an online magazine of some sort run by a restaurant, but one of its many features is lists of synagogues around the world.
For Chabad Lubavitch Centers around the world. Chabad Houses are great places to stay or eat on Shabbos, or just to get connected to Judaism and Jews. (Or try this link, for an alternate search engine at the same website.)