We have two websites.

Lasvegas
NewYork

we want to make sure the people registered at las vegas are able to login to new york site and people registered at new york site are able to las vegas site...

the problem is that we don't want to share databases... because we want the users of both the websites different as we want to send them information about particular city.

so that Las vegas users should only receive information about LV
and New York site users should only receive info about NY.

With Jms Multistites, it is not possible to share partially the users.
If you decide to share the users between lasvegas and newyork this mean that physically, you will have the MySQL table for the users only once in the DB with all the records (the users).
This will give the users the possibility to logn on Newyork or Lasvegas.

This will not share the whole DB but only the MySQL tables used by the users (session, access control and users).

I don't know what you mean by send sepecific information to a city.
Does that mean create specific articles or send email to all the users present in a websites ?

If you are using NewsLetter application, you can define distribution list.
So perhaps this is what you expect to do.