Localized SEO

I'm curious, we serve clients worldwide, but the only sites we have been able to get seen lately are those from the US, where we operate from and where our websites are hosted.

Would the location of our server be a hindrance to any SEO efforts outside of the country and do we need a local domain name to be indexed for those countries?

Yeah, Google looks at the location of your server as a factor when they determine serp positions.

YOu don't have to have a local domain but I find that a local domain tends to rank better for its local google.

Bear in mind though that the opposite is probably true and a .co.uk for example will find it harder to rank in the US