Hi Sasha - just two things: 1). Your website designer probably doesn't need to be near you, as it can all be done remotely. There is at least one thread on website design options on here. 2). Be careful if anonymity is important to do, because your name will be linked to the domain name (unless you've done it via e.g. a company name) and anyone can search for it.
But yes, I think many of us would say day times are busiest, but there is plenty of work at weekends and evenings too, especially if you can be ready for the after work crowd.