The quality of life would be great - you're thinking an order of magnitude too small for the size of a colony ship. Any society that is capable of building a colony ship could easily scale it up and definitely would want to for many reasons. They will have populations equivalent to large terrestrial cities and contain as much physical volume, industry, agriculture and entertainment as large cities if not more.
People can easily spend their entire lives inside the limits of Manhattan and never suffer for it.
Would it be a good guess that you've read
Cities in Flight, by James Blish?
Why would you get bored? Or rather, how? An infinite life span means infinite possibilities. You'll be able to do anything you want with decent long-term planning. Eventually you'd be able to do anything you want even without planning as technology improves to the point where we will reach a Star Trek-like state of resource availability. Money will become obsolete - all we need is better across-the-board technology and we will erase scarcity.
We're already on the exponential curve of technological growth, the point of economic liberation I'm talking about probably isn't more than a century off in my estimation.
Why do kids get bored in a roomful of toys and a playground across the street? There are some nights when I sit here in front of my computer, Wikipedia just a couple of clicks away, I'm surrounded by books, fanzines, and DVDs, I have Netflix, and I just feel so bored that the only thing I can think of to do is either to read an Archie comic or go to bed. I've got over a thousand books in my personal library that I've never read, yet what I'm reading right now is a book I've read a dozen times already.
I'll admit that part of the problem is that I've had issues with clinical depression for many years. When it's really bad, I can barely muster interest in anything. If it weren't for the cats needing food, water, and litter box cleaning, there are some days that I wouldn't bother getting up. So there could be all of my favorite entertainments and activities right at my fingertips, and none of it would matter. I should think that anyone living on the ships or colonies you're imagining would have to be fully screened for such things as depression and other forms of mental illness. Hopefully by then a cure would be found for these things. Right now I wouldn't want an eternity of the sort of life as it is.
So with your moneyless society and infinite availability of
stuff, how would the economy work? This is an argument that's ongoing regarding Star Trek. Picard lives in his myopic little starship Captain bubble where he can have anything he wants, so he doesn't really want anything other than to "better himself." But of course it never occurs to him that not everyone is like that. You can't tell me that Joe Sisko, or even Robert Picard give their goods and services away free - they have to be compensated for their food and wine somehow. And what if everyone on Earth decides they want to live on a humongous estate, instead of in apartments? There isn't room for everyone to do that, unless Earth has many billions fewer people in the 24th century. Picard is so used to the "no money" thing that when he and Ro Laren are posing as a client and prostitute in a bar on a border colony, she has to remind him that he's supposed to produce some coins and haggle for her fee.
Even in Kirk's time, there was money (I don't care what he said in the fourth movie; they might not use cash, but they damn well use money in some other form).
So how would unlimited stuff and infinite possibilities for activities work in a city-sized spaceship? Severely limiting population growth, or zero-growth, as in Bova's Saturn/Titan novels? If it's limited growth, you'd have people applying to have children, and who gets to decide if they're allowed, and what would the criteria be? For that matter, if everyone is immortal, why even bother having children? (interesting side note: in the TV series
Highlander and
Highlander: The Raven, the Immortals are all sterile, even before becoming immortal; none of them can father or bear children)
The ships will be massive. There really wouldn't be a single point of failure - the chance of one of them blowing up is about the same as NYC getting hit with an asteroid tomorrow. It's conceivable but highly unlikely.
As to boredom and lack of entertainment, again I point to NYC and ask if you really couldn't make a go of staying there forever? Because that's what a colony ship would be like. Only bigger, more advanced and with all the modern features.
Plus you guys act like it will be cut off from Earth. It never would be! It'd be in constant contact and though the time lag will get extreme, no colony ship would ever be truly isolated in every sense of the word.
Assuming people would want to go to NYC in the first place... I assume there would have been an immense change in society to eliminate crime, or you'd have street gangs and organized crime out in space. And please don't say that in a post-scarcity society there won't be any crime because people will have everything they could possibly need or want. It's human nature to test the rules and break them. Do it out in space and the result could mean a very nasty death for everyone.
Time lag... have a long enough time lag and you get problems. Who is in charge of these space cities? Are they completely autonomous, or just part of a central government? If the latter, I would say that C.J. Cherryh had it pegged when she said that the farther from Earth a colony or space station was, the less relevance Earth had in issuing orders and setting rules. That's a recipe for eventual rebellion and war.
I am of the opinion that given enough time, people can and do change. Given infinite life spans, people will have time to adjust to, accept and eventually become comfortable with all sorts of other people and ideologies. Take gay marriage acceptance - sure dying old people helped society progress but I personally know a lot of older folk that came to terms with it and even accepted it as a good thing just from being exposed to gay culture (if there is such a thing) over time. My own grandmother made such a transformation in the 4 years I lived with her.
Elderly people aren't part of a hive mind any more than any other age group. Take my grandmother and great-aunt, for instance. You know the phrase "raining like cats and dogs"? The rest of that saying is disgustingly racist by modern standards. Back in the '80s I explained to her that if she said that in public, people would be shocked and disgusted, and call her a racist. She didn't understand at first, but finally was able to eliminate that part of the saying from her vocabulary. I never heard my great-aunt say anything racist, ever. She was more old-fashioned than my grandmother in domestic matters, but she was also more enthusiastic at first about my then-new interest in science fiction. She gave me a Star Wars blanket and an astronaut-themed binder "for your outer space stories." (I still have those)
I do take my hat off to your optimism. Optimism is necessary for humans to survive and get off this planet. But human nature would have to undergo quite a change to make this scenario of yours possible.
