I am looking for a word that quickly describes someone who knows everything that is going on in the in the city they live in. This person does not engage in gossip concerning other people's personal lives, but rather is someone who knows what the weather is going to be like today, what sales are going on, what events are going on, and what happened in the news. They could tell you things like, "Store A is the best place to buy meat, but if you want vegetables is store B. If you want to buy dog supplies, you normally want to go to store Y but today there happens to be a sale on dog treats at store Z. There's a 5K going on tomorrow at 2:00, and there's a band concert at location X later that night." This person is not over dependent on technology for this information, as she gets most of it by "getting out there" and being involved with the community.
au courant In your example: Jane is au courant on where to go and what to do in Boston.
Definition from Vocabulary.com
To be au courant is to be well-informed about something. If you're au courant with local politics, you follow your city's elections and political controversies closely.
This word means being up to date on a certain subject. If you're au courant with a TV show, you've watched all the episodes, especially the most recent ones. Lawyers need to stay au courant on legal matters, and doctors need to be au courant on the latest medical research. In French, au courant literally means "with the current," or "in the course." If you stay with the flow of current events, culture, or work, you'll always be au courant. (emphasis added)
That person is "well-informed", socially "well-connected" or, as mentioned by Dan Bron in a comment, they are "plugged-in".
"well-informed" - having a lot of knowledge or information about a particular subject or things in general. e.g. How well-informed is the customer about the range, quality, and cost of the products on offer?
"plugged-in" - to be in the know of a certain subject. e.g. Yo dog, thanks for introducing me to that guy. He'll keep me plugged in on what's happening.
urbanite : a person who lives in a city
which, despite its bland definition, often has the colloquial association of someone who is an active consumer in an urban environment, is involved and enthusiastic about their city, and, depending on the context, could be considered 'hip'. For example, 'young urbanites' would give me the impression of millenials that frequent the hip parts of town, engage with their city, could give advice on what to do, and generally known to be in the know.
For an exaggerated context (not exactly what you're asking for, but it could be relevant), try
socialite : someone who is well-known in fashionable society and is often seen at parties and other social events for wealthy people