The threshold question is whether this case should be filed in LA or in AZ. If the contract was formed in LA, then the proper jurisdiction is LA and you would not have to spend the time and effort to go to AZ. Your damages will depend on the law of the State. In California, if you prevail you may be able to collect trebble damages for the cancelled check and additionally, you will be able to add interenst at the legal rate of 10% to the damages.
I am not responding based on Arizona law or California law but rather on general principles of law and legal practice. The law which applies in your case is not clear to me, and in any event may differ from these general principles, so if you need legal advice, you should consult a lawyer who practices in the jurisdiction where you will be litigating.
Typically "costs" are awarded to the prevailing party. These include the filing fee, witness fees (but not, typically, expert witness fees), fees payable to court reporters and the cost of transcripts, etc. Usually "costs" don't include traveling to the jurisdiction or the cost of a hotel room during the proceedings.
However, I also suspect you are litigating this in a small claims court. The upshot of it is, if you don't ask for an award of the cost of your plane fare and hotel stay, the court probably won't award it. However, it can't hurt to ask, because small claims courts sometimes award these kinds of things (even if they shouldn't).
Assuming you win, however, the next hurdle will be collecting on the judgment. Not always the easiest thing to do.
Not legal advice as I don't practice in California or Arizona. It's just my two cents. Please consult a lawyer licensed in one or both of those jurisdictions if you need legal advice.
First of all, if you are being sued in Arizona, Arizona law would apply so you may have to re-post your question under Arizona.
Secondly, it is not clear from your question whether the lawsuit is a small claims court lawsuit or a regular civil lawsuit. Your entitlement to "costs of suit" will depend upon the level of court in which the case will be heard.
Thirdly, as a general matter, costs such as travel and lodging would not be recoverable in a civil lawsuit.
Fourthly, check to see if you have a written contract with the other party which contains an attorney's fee provision. If so, then the prevailing (winning) party would be entitled to recover attorney's fees in addition to costs.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, consult with your own attorney.