I'm planning on starting a forum for the city I live in, with vBulletin software. What sorts of things would be useful on a local forum? Certainly I could add the time, and I'm sure there have to be widgets available for the weather...

I'd add topics of interest to your local community. Time and weather are not it. What kind of things does your community discuss? What kind of things would be of interest to them?

time, movies, local events, links to facebook etc. i'd say something like yahoo would suit your needs. checkout what they got

Places of interest, nice cafes and restaurants, events, sports, get to know each other session, etc

Local events and about the nature of your area would be better topics

Some interesting topics that would really interest the visitors like nature,movies etc

Yeah, it'd be better to talk about things that make the community interesting and unique. Are there some local fairs, farmers' markets, or shops that are completely unique to the city? What holds the community together? What could be a controversial issue that people will want to voice their opinions about?

Give them a space to feel like they are part of a community, rather than just living in the same place.

Include some community activities in it. You can also put some general issues in your place, problems, cool places and future plans. I'm sure that will be fun.

I never actually thought about something like that. Sounds like a cool idea. Topics I'd include:
Local News, General chat, place for business opportunities(employment, jobs, etc), place to talk about local businesses, general business talk. Also what is your city's niché? Like my city is huge on wines and fruit. So ideally I'd have topics dedicated to it. Nice restaraunts, maybe include a rating system? Maybe a special event forum for upcomming concerts, gigs, shows, comedy, etc... Or a forum dedicated for the community togethor to throw on activies togethor?

That's it from me... Hope it works out for you. I'd be very interested to hear back from you if you do find success. I think it's a great idea!
Good luck!