Does where my site is hosted affect SEO?

Only very slightly, and mostly through the physical distance a request has to travel. Server location is not treated as a direct geo-targeting signal in the way many site owners assume. Google has been explicit that it uses other, far more deliberate signals to work out which country a site is aimed at, and none of them require your server to sit in that country.

What actually tells search engines which country you are targeting

• A country-code domain extension — a .co.uk or a .de is a strong, explicit signal for that country, independent of where the server physically sits.
• Search Console's international targeting setting, where available, lets you state a target country directly for a generic top-level domain.
• hreflang tags, for a site serving multiple countries or languages from the same domain, tell search engines which version to show to which audience.
• Content itself — currency, address, phone format, local terminology — is a signal search engines read directly from the page.

Server location sits well below all of these in how much weight it carries.

Where location does make a real difference

The one place it genuinely matters is latency: a visitor a long distance from your server experiences a slightly longer round trip for every request, which can show up in load time. On modern hosting this effect is small for most audiences, and it is one a content delivery network can reduce for a global audience regardless of where the origin server sits — see why your website is slow for more on what actually drives load time.

In short: choose hosting for speed, reliability and support, not for the country its data centre happens to be in. That decision has almost no bearing on where your site is deemed relevant.