Specific number and date predictions are almost never borne out by actual events. "It's hard to make predictions, especially about the future."
I think large scale activities further out in the Solar System might take until late this century. But near Earth and Lunar endeavors will blossom in the next few decades, though I doubt they're reach the hundreds of billions in business done by then.
As you said, robotics, materials processing and small scale custom manufacturing will play a large role; already, multiple proposals for a Lunar base and a crewed Mars landing are driving more innovation in those fields. Given the difficulties recently experienced in asteroid sample returns, mining small bodies will probably lag behind at first, though they have the potential to outpace the Moon in some areas of material extraction.
Other areas just begging for expansion are space debris cleanup, test beds for human habitation such as stations with centrifugal sections, Earth and space based attempts at fairly self sustaining life support biospheres, and perhaps space solar power if we can manage to come up with both radiation-resistant long wear photocells, and a cheap means of manufacturing them in bulk. A bit longer term, Lunar ice mining and processing for rocket fuel.
I consider things like space hotels a much longer term endeavor. They probably won't happen until large scale space construction becomes much, much cheaper. The super-rich who will be their primary customers are just not numerous enough or reliable enough to support such an expensive industry. Human life support in space is a goal, not a means to a financial end. Space won't become a tourist trap for quite some time.
As far as real space colonization goes, IMO that might be semi-plausible by mid-century, more likely the three-quarters mark. It will require a matured industrial infrastructure capable of both building and maintaining the necessary habitats.
"I'm planning to live forever. So far, that's working perfectly." Steven Wright