I developed a version of a client's main website in Hebrew. Most of the Hebrew site visitors will be coming from Israel. My server is fast in the States but sluggish in Israel (per some ping testing).
How can I speed up serving the site to Israel?
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Find a web host nearer to Israel; it will decrease the ping time and therefore page load time will go down too.
For a more complex solution, you could serve from the US server to people in the US, and anywhere in Europe, you could serve from the other server. (more info)
This is an old question; the answer in 2019 is to use a distributed content delivery network. There are several contenders, though the favorite for many small web sites is CloudFlare because they have a free tier which should work fine at least until you have a better understanding of whether this is sufficient for your requirements.
Any CDN will cache your static content on servers close to the clients, and take care of passing through any dynamic requests to your origin server. A nice bonus with CloudFlare is that they have DDoS mitigation and easy support for Let's Encrypt.
One option which is certainly more complicated is to duplicate the website and put it on two servers, It won't really help with ping time IMO because all request will first have to reach your server which will then redirect them to the Israeli server. (I assume you don't want two separate domains for the landing page)
This can be done with a 301 redirect to another subdomain for example so the browser will cache the subdomain after the first visit so on the second visit the redirects will already be cached and occur automatically
EDIT: according to comment here it's possible to have two DNS servers for one website, I've not done that but if you decide to host on two servers this will certainly help. If you do this the 301 will not need to occur as well saving more time
The big problem with this approach is if the website has a database and you need to keep a synchronized database between the two servers.
If this is not a problem or you don't mind doing this than the first approach can be good.
Another option which can be regardless of the previous (you can do either one or even both) is to use a caching service / CDN, there are some free ones and some paid ones.
This just makes everything faster for everyone and is always good to try when having latency issues.