San Francisco in the beginning of January

Last year in 09 these events where popular.

1. January Festivals & Fairs
2. San Francisco Inauguration Parties
3. January Museum Exhibits
4. Live Music - Club Calendars
5. Winter Birding in the Bay Area

Also Eventful has a date picker here for events in the city

Here are my preferred ways of searching for events:

• Yelp events
  Scroll down to "Other Popular Events" and select Jump to date to search a particular week. Keep an eye on this page, though, as events are posted fairly often.
• EveryBlock
  Subscribe to a customized feed for the area you want to spend the most time. You can specify the type of feed item, so if you're visiting, you'll probably want to filter out city maintenance requests and such.
• FunCheapSF
  Very good list of events. This can be useful even if you aren't on a tight budget, because it's less focused in scope and so you may happen across something fun that you wouldn't have considered otherwise.

I'm guessing that if you have a favorite artist in town, you would just search for that name. So here's my suggestion regarding shows: check out some well known venues in the city and take a chance on artists you're less familiar with, at least once. About.com has a good list of well-known venues, as well as links to their upcoming calendars.

I don't go to a lot of shows, so I can't tell you much about that list. Slim's was pretty good; I saw a rock show there. The drinks were a bit expensive, but tickets didn't cost much to get in. I've heard the most about Amnesia, Cafe Du Nord, The Fillmore, The Independent, and Yoshi's, so if you can't decide, you could start by looking up those places.

Warning: whatever you do, don't attend a concert at the Concourse! I've only been there for a convention and it was adequate for that, but it's clearly a terrible place for music, as you can see by the awful Yelp reviews.