This is hard to say, given that the need to visit places like the moon isn't very high at the moment. I'm assuming by "ordinary people" you mean people traveling there as tourists or vacationers. For a trip to the moon to be relatively common and cheap enough for the average family to afford, there will need to be some profit in it for private companies or governments will have to want to send colonists there, much the same way European countries were colonizing the Americas centuries ago.
Assuming that colonists would go first (and using the colonial era of Europe as a sample) we can estimate when this would occur. Columbus reached the Bahamas in October of 1492. We can consider this event analogous to the July 1969 moon landing. The Spanish established their first colony just four years later in 1496. Here we are 51 years after the first moon landing and still no colony, why?
The reason is that the Spanish had many reasons to colonize while modern humanity has very little. The Spanish wanted to explore the new world, while we can explore the Moon without physically going there. The Spanish wanted to expand their empire, while the moon is a neutral territory thanks to the 1979 Moon Treaty ( more on that here: https://en.wikipedia.org/wiki/Moon_Treaty ).
The short answer then is any nation that wanted to go would have to deem it necessary to start mining the Moon and then get UN approval to do so. That nation (or more likely nations) could then send colonists to the Moon and start constructing the necessary infrastructure. We have the technology to do most of that now but we are still not certain if the human body could handle being in low gravity for an extended amount of time. All-in-all I would give any Moon colonization effort: 5-60 years before a nation(s) decides to actively pursue it, 0-10 years for the UN to approve and sanction such an effort, 10-30 years to build a colony/mining operation on the Moon's surface and then we would be ready to start populating the colony.
All together I would estimate anywhere from 15 - 100 years before people are ready to colonize the Moon's surface. That would put the timeline as anywhere from 2035 - 2120. If I had to give a specific year I would say 2100 with a huge uncertainty.