Of the three choices I'd go with below the monuments but important-ish, but more precisely I'd put it below a lot of other races.
First of all, I'm not interested in what "the cyclists" or "the fans" or "the people" or anyone else thinks - I look at it as if I were a cyclist. And for several reasons, the Olympics wouldn't really be on my radar.
For one thing, cycling is the world's most beautiful sport, and it's the world's most beautiful sport for several reasons which won't fit into the Olympic mould. The great stage races and one-day races are more than just physically and psychologically demanding sporting events. They are journeys through a region or a nation's political geography and history; where the scenes of sporting combat take place on the roads of military conflict, national frontiers, sectarianism, religious devotion, scientific discovery, recent and historical tragedy, the urban and the rural, industry, engineering marvels, modernity and museum, great locations in film and television, and a healthy dose of tourism promotion and local politicking. It's not always alluded to, it sometimes goes unspoken, but it is almost always there. Even as the race routes change, they are irreversibly soaked in these characteristics. In other sports these are peripheral attachments, but I don't know any sport so conscious of its relationship to the past and present of the society around it, where these things take a front seat in what makes a race happen, and often in what makes a race great. Most sports just happen in a place made for that sport to happen. The nature of great bike races - even new ones - makes them journeys beyond merely what the score is at the end.
The Olympics doesn't have this. I mean, in theory it should. It happens in places where history and poltics and culture exist, but they aren't emblematic of the event. We're supposed to put all that stuff to one side, in little television inserts and tokenistic newspaper articles about the host country, boxes where it can be fetishised safely away from "the sporting spectacle" and "the Olympic values" of gutless faux-apoliticism.
You might think, "Well the World Championships is just a nomadic circuit race too, what's the difference kid?"
Well, yeah it is. It's one of the reasons why I don't rate the Worlds as highly as most people do - well below the monuments, and below a lot of other one-day races too, in fact. But the Worlds does have something that the Olympics doesn't have, and that is that it's ours, goddamit. It's put on for us. No bill-sharing with synchronised swimming; no being tacked-on to an event which doesn't really care whether we're there or not; no generic medals, those non-descript symbols of a sport being crushed into conformity with what the public is supposed to understand a sport to look like. Those rainbow bands say This Is Cycling.
(Okay, the Worlds does have the medals, but come on, if you won the Worlds and you had the choice of gold medal or rainbow jersey, you know what you'd choose.)
On the non-romatic, entirely sporting side of things, the Olympics has a small field (a pathetic 67 riders at the Beijing women's race). You could make the argument that this means it's somehow more elite, but in reality it means a lot of great riders with something positive to bring to the table just don't show up. It's a nice opportunity for the non-traditional cycling countries, but it would be even nicer if they had a few more riders around like themselves and could actually club together to make a break for it, rather than being relegated to near-certain solitary toiling.
Personally, as some who's pretty unpatriotic I'm also not a big fan of the national teams setup. I like the Brits to do well because it might lead to more interest in cycling in Britain, and when it comes to the younger riders I often know more about the Brits than the other countries so I have a bit more of an emotional investment in them. But by and large I see national partisanship as pointless. So to me stuff like the Worlds and Olympics feels a bit like cycling on holiday. Mix in the other factors I mentioned about the Olympics and it starts to become something I don't really recognise as my cycling at all. Pseudo-cycling. It's why I could never take Paolo Bettini's gold helmet or Samuel Sánchez' claims that his victory in the Olympics was more special than winning the Tour de France seriously.