Let's start with the general rule:

Just because it may be more convenient for you does not entitle you to sue in your home state.

The reason for this rule is grounded in constitutional law - no one should have to defend themselves against a lawsuit in a forum where they lack even "minimal contacts,"  and therefore have no connection with that State.

In that vein, New York's Long-Arm Statute, CPLR §302, provides, in pertinent part, as follows:

§ 302. Personal jurisdiction by acts of non-domiciliaries.

(a) Acts which are the basis of jurisdiction. As to a cause of action arising from any of the acts enumerated in this section, a court may exercise personal jurisdiction over any non-domiciliary, or his executor or administrator, who in person or through an agent:

1. transacts any business within the state or contracts anywhere to supply goods or services in the state; or
2. commits a tortious act within the state, except as to a cause of action for defamation of character arising from the act; or
3. commits a tortious act without the state causing injury to person or property within the state, except as to a cause of action for defamation of character arising from the act, if he (i) regularly does or solicits business, or engages in any other persistent course of conduct, or derives substantial revenue from goods used or consumed or services rendered, in the state, or (ii) expects or should reasonably expect the act to have consequences in the state and derives substantial revenue from interstate or international commerce; or
4. owns, uses or possesses any real property situated within the state.

So, in the breach of contract context, at what point does contact between the parties suffice to establish personal jurisdiction over the defendant?

In that regard, New York's courts have stated as follows:

"[S]everal factors should be considered in determining whether an out-of-state defendant transacts business in New York, including:

(i) whether the defendant has an on-going contractual relationship with a New York corporation; (ii) whether the contract was negotiated or executed in New York and whether, after executing a contract with a New York business, the defendant has visited New York for the purpose of meeting with parties to the contract regarding the relationship; (iii) what the choice-of-law clause is in any such contract; and (iv) whether the contract requires franchisees to send notices and payments into the forum state or subjects them to supervision by the corporation in the forum state. Sunward Elec., Inc. v. McDonald, 362 F.3d 17, 22 (2d Cir. 2004). "Although all are relevant, no one factor is dispositive... Rather, the ultimate determination is based on the totality of the circumstances." Id. Those circumstances include "[a]cts performed by a defendant subsequent to the execution of a contract…." Cutco Indus., Inc., 806 F.2d at 367.