Well I wouldn't live to have lived there but if there was the chance to travel in a time capsule and see something and walk around for the day etc, I'd have liked to have gone to South Africa in the days when the Dutch settlers first arrived. I went to Stellenbosch - which is a beautiful part of the world even now where there are buildings and roads etc, and saw some old paintings in a museum there that were painted in the 1800s, of the surrounding area and around the Western Cape when it was unspoilt, and it looked absolutely breathtaking, just boundless hills and rivers surrounded by the same mountains. I'd have loved to have seen it then.
In fact if you could do that time capsule thing I'd like to go anywhere really before things got very developed, I'm sure this country looked beautiful, and I'd have loved to be able to go out on a clear night when there was no street lighting, cars or any other light pollution and seen millions of stars.
As for a period to go to I'd quite like to have been back in time in the UK and been born in say 1972, then I'd be in sixth form in 1988-1990 right at the madchester rave era, grown up in my early 20s in 1990s Britain, gone to watch a few games in Euro 96, been 25 when Blair got elected, probably been in position to have bought a house in the late 1990s and taken advantage of the huge boom in property prices, and been able to get my career established by the time the drawbridge fell from underneath everyone in the late 2000s.