I suppose another issue is that I am so attached to them that I'm not ready to see them leave and really grow up. They've been with me for so long, you know...?
My advice (as the mother of one 23yo and one 19yo): make it easy for them to grow up. Don't make them feel guilty about it or afraid of hurting you.
Whether you like it or not, they live in a culture where they are supposed to start thinking of themselves are grown-up by the age of 18, and if they are conscientious young men they will want to live up to those expectations. That doesn't mean they won't want your advice or that you won't mean lots to them: it just means that you will have to work with a different dynamic.
Let them see that you are happy and proud to see them growing into independent young men. You want to see them grow up big and strong and part of that strength is gradually learning to make your own decisions. Let them know that you are there in the background, that they can talk to you, and that you will listen and help if they want help (or just listen if they don't), but that their growing ability to make decisions is something you value.
As for family activities, it may help if you accept that they will probably want to spend a fair bit of time with their peers (either face-to-face or via the internet). This is normal in any culture: to a great extent, young men learn to be young men from other young men.
But you can also encourage some family interaction: watching a show together or just eating a meal together.
Best advice (and already given by others): just be there.
Second best advice: let them see that your whole happiness does not depend on them, that you have friends and interests and a whole grown-up life that does not have to revolve around them. The best way to make them NOT want to spend time with you is to make them feel guilty about the fact that they are eventually going to grow up and leave you. Show them there is nothing to be guilty about: you will be fine.