It seems you have to file for the LLC in NY as domestic or foreign (foreign being a LLC that is registered somewhere else). The publication requirements are the same, so cost is not a factor. The LLC fee and bi-annual requirements are similar as well.
Since you have to file something in NY and the costs are similar, then I would think about where are most of your operations and employees. If that is in NY, I would file as a domestic LLC in NY. If your operations are in VA and you just happen to serve clients in NY, then a NY foreign LLC may be a better option.
Legally, if you have NYS and NYC sourced income, the state and city wants income tax on their share of NYS and NYC income. If your base is in VA, I am not sure how NYS would know you serve clients in NY
, but it is usually more costly to find that out from the state after the fact