what does 'second' mean here

I assume it’s an address?

That might be a location, not just second but the whole thing

American way of giving a location. Many of their city centres (downtowns) are big grids, and the streets are labeled with numbers instead of names. Most famously in Manhattan, but everywhere really.

Second Avenue. Given the phrasing and the reference to Chinatown, almost certainly New York, specifically Manhattan. People generally drop the “avenue” part, as well as the east/west parts of street names when it’s obvious. “ I live on 73rd and Third,” meaning “I live on [East] 73rd [Street] [at the intersection of or near] Third [Avenue].” There’s a Ramones song called “53rd and Third,” also refers to Third Avenue. Edit: this comment tells you a little bit about the character, by the way. 25th and Second is a perfectly fine place/neighborhood, if a little boring compared to other lower Manhattan neighborhoods. Before the Second Avenue subway line (which as far as I know is still not done), it would be *slightly* inconvenient for commuting (you’d have to walk to Lexington for the nearest subway). But it’s not particularly hip or cool. This character may be a bit of a snob, or considers themselves really cool and looks down on someone who lives in a less hip part of Manhattan.

Twenty-Fifth and Second is the intersection of 25th Street and 2nd Avenue in Manhattan, New York (likely)

Second street

no clue to be honest

It's an intersection of 25th Street and 2nd Avenue, in Kips Bay, Manhattan.

These are streets in NYC - more specifically their intersection.

If this is really NYC, then the author left something out. Since this is by Second Avenue, this would be East 25th Street. Streets in Manhattan have 5th Avenue as a divide between east and west. For example, if this was 25th Street on 6th Avenue, this would have West in front of it, so West 25th Street, since it's west of 5th Avenue. I know this isn't answering the question for "Second," but wanted to add more context to the passage above.

Fun fact – second is the most popular street name in America. Some cities/towns have First Street or Main Street and then Second Street. I think Third is the second-most popular

Why was "Second" confusing, but not "Twenty-fifth"? They're functionally the same. 

Why does the character hate Kips Bay? 😭 It's not that bad here lol

Street name/number/house number/location of some sort??

Second Street or maybe Avenue. It's common to just say the street name and omit the word "street" (or avenue, road, boulevard, etc.) when it's understood from context that you are talking about a street.

I hate this book

Why would you return to a restaurant where you get sick half the time? Nonsense

Those are street names. The intersection of two streets is often used as a general location.

“The corner of twenty fifth and second” is the meaning here. Those are street names (Though they very often are not that consistent) Some cities just spontaneously name the streets “1st 2nd 3rd James, Holloway, 4th, 5th” And you just have to remember them. It’s dumb and we get it, but it’s mostly a “you memorize it” case.

Segundo 

Twenty-fifth Street and Second Avenue. Street names. They are talking about a street intersection

I believe this means second (2nd) avenue referring to a street/road intersection in I’m guessing New York. I’m from the UK and can’t confirm if this is just a NY thing, but it is not a thing in the UK so most Brits would only understand this because we have seen films or TV from the USA where this nomenclature is used. Many native English speakers from outside of the USA would have no clue either.

I think it’s American way of noting intersection between horizontal and vertical street locations for an address.

Where 25th Street crosses Second Avenue. https://freetoursbyfoot.com/new-york-city-streets-and-avenue-grid-explained/