NaOH + HCl ---> NaCl + H2O

is that what would happen?

yes

How would I find the molar enpalthy of this reaction?

I note that you have posted a question above about the heat of the reaction and I have responded how to calculate q. If you are going to molar enthaply, it REALLY would be best to post the entire problem than to try to do it piece-meal. You posted first about NaOH + HOH, NaOH(aq), next about balancing it, next about the equation NaOH + HCl products, then this about the enthalpy. It is laudable to try to work this out in steps BUT it puts us in the position of working a problem in pieces without knowing where we are going. Sometimes there are multiple paths to take and our answer may not take you where you want to go if we don't know where we're going in the final question.

Yes, that is the balanced chemical equation for the reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl). The reaction produces sodium chloride (NaCl) and water (H2O).