I don't choose RPGs by time periods but current day is probably my favorite. I find very interesting to see modern objects and places by the RPG prism. Ninten, the Earthbound Beginnings protagonist can get an asthma attack when fighting cars because of the smoke and to dispell its effects you need to use an inhaler. Also, exploring the country in the game made me remember when I was a kid.
Many SMT games are set into current day also. Strange Journey used the modern themes very well. Unfortunatelly, there aren't many RPGs in current times or near future. Would love play a military RPG, something like Front Mission.
My second favorite is post apocalyptic. It has the locations and tools of the current times, but with the freedom of an world in chaos.
That said, I don't dislike any time periods. If it is good, I'm in. Dragon Quest, Final Fantasy, Dark Souls, Morrowind, Dragon's Dogma are among my favorites. I wish we had more variety in setting though.