If you want to have a non-country-specific website in English, what is/are the best time-of-day to run the maintenance? You can also answer by specifying what is the worst time-of-day to run the maintenance, as everything else is then "better". My websites will be more toward leisure then business.
This isn't a question with a hard and fast answer, in fact none of us can tell you when to run your maintenance, just give you a few pointers to finding the answer for yourself.
First of all, when you say "maintenance" what do you mean? Are you saying the site will be offline at this time? That it will run slowly at this time while you run a lot of background jobs? Are you saying that content is processed in batches and this is when each day's batch of content updates are run? That you do backups at this time?
What will the impact of this maintenance be? There's a big difference between "my site will run a little slowly" and "my site won't run at all", and if its the latter then you need to either work around this with a better system that doesn't take your site offline or a load balancing system so you can keep the site itself available while taking parts of your infrastructure offline for maintenance.
Anyway, talking about maintenance schedules: The "best" or "least worst" time of day is what you determine yourself from looking at your site's usage. Anything else is bogus as English is used throughout the world so visitors to a non-country specific English language site can come from anywhere in the world at any time.
Until you can gather some data, it might be worth considering where you consider your audience will probably come from (even though people can use an English language site from all over the world, do you expect your users to mostly come from USA? UK? Australia / NZ? Elsewhere?) and try for an early morning (3am) time slot in that audience area.
I should add a link to this question from stack overflow, which has some interesting comments you may find helpful, and please take this quote into account in particular:
Being in Australia, the middle of the day on Monday, one of the busiest times of the week is normally when service operators based in the US (as it's Sunday night there) decide to do maintenance. I realise that services like SO and Google Wave are free so fair's fair but especially when Campfire went down I thought, "Surely we pay the same as any other client for this application and can therefore expect the same level of service?"
You really need to analyse your site's usage and choose an appropriate maintenance window based on what you discover. You don't say which web server you're using but if you search for a log analysis tool for your server then you should find something that will give you an idea of when your site is least used/most used etc.
Impossible to answer, we have no access to the statistics of your website so we don't know when it's quiet. It also depends on the total downtime because of the maintenance. When the site will be down for a minute, you can do it during office hours. But when the site will be down for 5 hours, that's a different story.