There can be different reasons for hosting your website on a server located in your country.
Let me first lay my cards on the table. I've been hosting websites (websites for both clients and myself) since 1999 and have had experience with servers located in the United Kingdom, the Unites States, Australia, Spain and India so my advice is based on what I have encountered over these years.
The location of the web hosting server determines the country to which the website belongs. Several search engines, Google included, assign a country to a website based on where it is hosted.
So if you have a country specific domain name or want to rank high on local search engines, you can put your website on a web host located in your country. By the bye, servers in the United States (and elsewhere too) can host country specific domain names. Though its debatable, a country specific domain name hosted in the same country can lead to better rankings in local search engines. At least it seems pretty logical, doesn't it?
If web hosting is cheaper in your country, go for it. However, before you decide on the web host, be sure to ask around or read reviews on the web. Do not try to pick up the cheapest web host but rather one that provides good service and you can come to know of this by reading that company reviews on the web or in magazines.
I don't think managing a website located in your country is easier than managing one abroad. It's the same! However, if you feel that it is easier to approach the support and technical staff, over a local phone, for example, I would suggest that you host it locally. This is especially true for beginners; getting quick support and troubleshooting for your website will always be of great help when you are just starting out.
How quickly a website loads depends on several factors including the net connection of the web server and that of the client (visitor). If all factors are constant, I don't think there would not be any substantial difference in loading speeds for a website hosted locally and one hosted in another country, esp. if most of the visitors use broadband Internet connections.
If most of your prospective visitors are from your country, should you load your website locally? The answer is actually, in direct. It is speculated that certain local search engines might be giving a ranking boost to websites located in the same country. If so, and because your prospects are from your homeland, you should host the website locally. This would definitely be a good idea if most of your countrymen use local search engines, for example, using google.co.uk instead of google.com.
Finally, I am not sure why you would like to host a website in your country simply because it's in the same time zone. If that makes you happy, go ahead.
Page contents: Is it beneficial to host a website on a server located in your country? this article provides a detailed answer to a common web hosting question.
Comments, questions, feedback... whatever!