City is asking me to give them an easement through the side of my property. What are my rights on this?

Your “rights” are going to be a factor or your state and locals laws and ordnances.

Some states ‘ask’ and if you say"no", they take it by emminent domain…go to the city in person and ask.

Usually, they want to install something ‘common’ to several users, like a water or sewer line.