To do well in most regional Googles, you need EITHER a local tld OR local hosting; in some cases, both.
You may need to decide if your site is 'international', or could better be subdivided into several regional sites.
Both approaches have plusses and minuses.
Whatever you decide, local content is a key to success. Local links alone will not do the job (though they may help).
Points to consider include whether you have local addresses / phone numbers, whether you need / want / could deal with local currencies, and whether you qualify for / want / can handle a selection of local sites around the globe.
And if subdividing will help / dilute your offering / confuse visitors / get you into duplicate content issues
Sadly, there's no 'one size fits all'; it's what suits your business and your potential customers best.